CAIMS_SCMAI Canadian Symposium on Fluid Dynamics

June 24-28, 2012
The 2012 Annual Meeting of the Canadian Applied and Industrial Mathematics Society

Home

Committees

Plenary and Prize Speakers

Public Lecture Speakers

Registration

Submissions, Minisymposia & Abstracts,

Scientific Program

Venue

Hotel & Housing

Travel to Toronto

Toronto Information

Abstracts

Tahmina Akhter, Ryerson University
Role of Compressibility and Slip in Blood flow through a Stenosis

One type of blood disease is the narrowing of a blood vessel known as stenosis, and high cholesterol is one of the main causes for this. Suitable mathematical models are important to describe the resulting effect on blood flow, and to study the problem analytically, as well as numerically. An approximate analytical solution for compressible flow through a stenosis will be presented and compared to a numerical solution obtained using a particle-based method called Multiparticle Collision Dynamics (MPC). Results will be shown for various degrees of severity of the constriction, various Reynolds numbers, and slip as well as no-slip boundary conditions.
Back to top

David Amundsen, Carleton University
Resonant Response in Acoustic Wave Systems
Coauthors: M. Mortell (UC Cork), B. Seymour (UBC), T. Shatnawi (Carleton)

The response of acoustic wave systems under resonant, or near-resonant, forcing is well studied and has implications for a range of industrial applications. Classically such problems are associated with shocked profiles which rapidly manifest even under weak forcing. Recent studies have shown, however, that when features such as geometry or underlying density stratification are varied, the shocks may be eliminated and continuous resonant solutions arise. The nature of the transition between these two regimes is not well understood. Through consideration of a particular class of simple, axisymmetric geometries I will present some preliminary results and insights into the connection between these two qualitatively distinct outcomes.

--------------

Youssef Belhamadia, Universisty of Alberta
Numerical Modeling of Phase Change Problems with Convection
Coauthors: Abdoulaye Kane and André Fortin

Phase change problems with natural convection play a significant role in several industrial applications. The main challenge is to accurately compute the liquid-solid interface where phase change occurs. This phase change boundary is time dependent and its morphology can be affected with the melt flow. In this work, an enhanced formulation based on the enthalpy-porosity method is proposed where the different thermophysical properties between the two phases can be easily taken into account. Accurate temporal and spatial discretizations are also employed for solving the proposed formulation. Numerical simulations are presented and compared to the experimental data to illustrate the performance of the proposed methodology.
--------------

Yves Bourgault (University of Ottawa)
Domain Decomposition Methods for Modelling Mass Transfer in Fuel Cells
Coauthors: Hamidreza Khakdaman and Marten Ternan, University of Ottawa

Mathematical models of mass and charge transfer in fuel cells give rise to a system of nonlinear partial differential equations (PDE). These PDE must be solved over sub-domains representing the anode, electrolyte (membrane) and cathode using coupling transfer boundary conditions. The implementation of the usual transfer boundary conditions within a Schwarz domain decomposition method with finite element discretization did not turn out to be effective. We are proposing as an alternative to use Neumann-Neumann coupling boundary conditions at the membrane/electrode interface. Special care is required for proton conservation as Neumann boundary condition are needed on all exterior boundaries and the ground state of the electrolyte potential must be properly set to ensure an equal total reaction on the anode and cathode sub-domains. The numerical strategy adopted and numerical results will be presented.
Back to top

--------------

(c)Lydia Bourouiba, Massachusetts Institute of Technology
Energy transfers in rotating turbulence

Turbulent flows subject to solid-body rotation are known to generate steep energy spectra when two-dimensional columnar vortices dominate. The dominant mechanisms leading to the accumulation of energy in the two-dimensional columnar vortices remain undetermined. Here, I will discuss the discreetness effects that could arise and affect the energy transfers in rotating flows when examined in finite and periodic domains and discuss the scale-locality of the nonlinear interactions directly contributing to the growth of the two-dimensional vortices. Implications for existing theories of rotating flows will be discussed.
Back to top

--------------

John Bowman, University of Alberta
Coauthors: Malcolm Roberts
Pseudospectral Reduction of Incompressible Two-Dimensional Turbulence

The turbulence decimation technique known as spectral reduction was originally formulated entirely in the wavenumber domain as a coarse-grained wavenumber convolution in which bins of modes interact with enhanced coupling coefficients. A Liouville theorem leads to inviscid equipartition solutions when each bin contains the same number of modes. A pseudospectral implementation of spectral reduction which enjoys the efficiency of the fast Fourier transform is described. The model compares well with full pseudospectral simulations of the two-dimensional forced-dissipative energy and enstrophy cascades.
Back to top

--------------
Robert Bridson, UBC Computer Science
Coauthors: Tyson Brochu (UBC) Christopher Batty (Columbia) Todd Keeler (UBC) Essex Edwards (UBC)Surface Tracking, Triangle Meshes, and Fluids in Movies

We consider recent developments in our dynamic triangle mesh front tracking method, as embodied in the El Topo software. Our general approach to avoiding the trickiest potential mesh tangling scenarios is to never allow the mesh to self-intersect, resolving motion-induced intersections with contact handling algorithms adopted from solid mechanics in the worst case. This lets us efficiently track extremely thin and extremely complex volumes efficiently and robustly. We highlight its application to incompressible flow for visual effects in film, particularly free surface water (where topology change is one of the biggest challenges), as well as smoke and fire (where standard methods run into systems problems in film production).
Back to top

--------------
Walter Craig, McMaster University
On the dimension of the Navier - Stokes singular set

In the hypothetical situation in which a solution u(t, x) of the Navier-Stokes equations in three dimensions develops a singularity at some singular time t = T, it could do this by a failure of regularity, or more seriously, it could also lose energy through concentration. The famous Caffarelli Kohn Nirenberg theorem on partial regularity of weak solutions gives an upper bound on the Hausdorff dimension of the singular set S(T). I will describe a microlocal lower bound on the singular set, given in terms of local properties of the Fourier transform of the solution. The first result is that, if the singular set is nonempty, then there is a lower bound on the dimension of the wave front set WF(u(T, .)) associated with the singular set S(T), namely, singularities can only occur on subsets of phase space T*(R^3) which are sufficiently large. Furthermore, energy concentration at time T implies that the solution is discontinuous in L^2, for which we identify a closed subset S'(T) of the singular set S(T) on which the L^2 norm concentrates at time T. We then give a lower bound on the microlocal manifestation of this L^2 concentration set, which is larger than the general one above. An element of the proof of these two bounds is a novel global estimate on weak solutions of the Navier-Stokes equations which have sufficiently smooth initial data.

--------------
Hans De Sterck , University of Waterloo
Coauthors: Lucian Ivan, Scott Northrup, Clinton Groth
Hyperbolic Conservation Laws on 3D Cubed-Sphere Grids: A Parallel High-Order Solution-Adaptive Simulation Framework

A scalable cubed-sphere grid framework is described for 3D fluid flow simulations in domains between two concentric spheres. Our first main contribution compared to existing cubed-sphere codes is the design of a genuine multiblock implementation, leading to flux calculations, adaptivity, implicit solves and parallelism that are fully transparent to the boundaries between the six cubed-sphere grid sectors. This results in the first fully adaptive three-dimensional cubed-sphere grid framework, with excellent parallel scalability on thousands of compute cores. Our second main contribution is a high-order finite-volume method that is naturally uniformly high-order on the whole cubed-sphere grid including at sector boundaries. Cubed-sphere grids are gaining increasing prominence in a variety of application fields, including weather and climate simulation and astrophysics, and our work is at the leading edge of these developments in terms of parallel 3D adaptivity and high-order capabilities.
Back to top

--------------

Colin Denniston, University of Western Ontario
Coauthors: Frances MacKay, Santtu Ollila
Modelling Porous Colloidal Systems of Particles in a Compressible Fluid

We discuss the implementation of hydrodynamics interactions of colloidal particles through a compressible, thermally fluctuating fluid. We discuss issues related to ensuring the colloids react dynamically so that they have a well defined mass in immersed boundary types of simulations. Examples, such as shear melting of colloidal crystals and hydrodynamic entrainment of particles in a channel are used to illustrate the models.
Back to top

---
Matthew Emmett
University of North Carolina
Coauthors: T.B. Moodie
Formation of bed ripples due to the passage through the critical Froude number of dam-break flows

When a semi-infinite body of homogeneous fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier the resulting flow over a horizontal or sloping bed is referred to as a dam-break flow. When the bed is no longer stable so that solid particles may be exchanged between the bed and the fluid the dynamics of the flow become highly complex as the buoyancy forces vary in space and time according to the competing rates of erosion and deposition. Furthermore, when the Froude number of the flow is close to unity perturbations in the height and velocity profiles grow into N-waves and the bed below develops ripples which act to sustain the N-waves in the fluid above. It is our intention here to study dam-break flows over sloping erodible beds and the development of bed ripples.
Back to top

----------

(C) Mohammad Farazmand, Department of Mathematics and Statistics, McGill University
Coauthors: George Haller, Department of Mechanical Engineering & Department of Mathematics and Statistics, McGill University
Locating coherent structures in turbulent flows using the geodesic theory of transport barriers

We use the recently developed geodesic theory of transport barriers [Haller & Beron-Vera, submitted to Physica D (2012)] to locate a variety of Lagrangian Coherent Structures (LCSs) in two-dimensional turbulent flows. We review the numerical challenges in the implementation of the theory, and describe a numerical algorithm that addresses these challenges. The algorithm is in turn illustrated on direct numerical simulations of decaying and forced Navier–Stokes turbulence. In particular, we identify
hyperbolic barriers (generalized stable and unstable manifolds) and elliptic barriers (Lagrangian
vortex boundaries) in the flow. The latter barriers enclose coherent vortices that are more robust and live longer than typical vortices in turbulence. We also identify a systematic difference in the size of Lagrangian eddies in forced and decaying turbulence.
Back to top

--------------
Yanghong Huang, Simon Fraser University
Coauthors: Y. Huang T. Kolokolnikov, Razvan Fetecau
Swarm dynamics and equilibria for a nonlocal aggregation model

We consider the aggregation equation rt-?·(r?K*r) = 0 in Rn, where the interaction potential K models short-range repulsion and long-range attraction. We study a family of interaction potentials with repulsion given by a Newtonian potential and attraction in the form of a power law. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. The equilibria have biologically relevant features, such as finite densities and compact support with sharp boundaries.

(C)Razvan C. Fetecau, Simon Fraser University
Coauthors: Joint work with Angela Guo, Simon Fraser University.
A mathematical model for flight guidance in honeybee swarms

When a colony of honeybees relocates to a new nest site, less than 5of the bees (the scout bees) know the location of the new nest. Nevertheless, the small minority of informed bees manages to provide guidance to the rest and the entire swarm is able to fly to the new nest intact. The streaker bee hypothesis, one of the several theories proposed to explain the guidance mechanism in bee swarms, seems to be supported by recent experimental observations. Originally proposed by Lindauer in 1955, the theory suggests that the informed bees make high-speed flights through the swarm in the direction of the new nest, hence conspicuously pointing to the desired direction of travel. Once they reach the front of the swarm, they return at low speeds to the back, by flying along the edges of the swarm, where they are less visible to the rest of the bees. This work presents a mathematical model of flight guidance in bee swarms based on the streaker bee hypothesis. Numerical experiments, parameter studies and comparison with experimental data will be presented.
Back to top

--------------
Jan Feys, McGill University
Coauthors: Sherwin A. Maslowe
Stability of a Trailing Vortex

A similarity solution for an aircraft trailing vortex, valid far downstream of the wingtip, was found by Batchelor (1964). Its stability has been the focus of many papers, beginning with Lessen et al. (1974). Motivated by the recent experiments of Lee & Pereira (2010), we consider a family of profiles discovered by Moore & Saffman (1973) that better describes the axial flow deficit observed near the core of the vortex. In this talk, we present results for the latter profiles and compare the growth rates with those for the Batchelor vortex.
Back to top

------------

J.M. Floryan
Dept. of Mechanical and M aterials Engineering, The University of Western Ontario
Direct Determination of Control Actuation

Changing/modifying state of a flow requires an external input, which we shall refer to as control actuation. Actuation can be introduced either at the boundary of fluid domain or throughout the fluid volume. The magnitude and distribution of actuation determine the form of the new state. Knowing the desired state, it is advantageous to determine the required actuation directly. Unfortunately, this cannot be done as, typically, flow problem specification requires specification of the actuation first to be followed by determination of the corresponding state. Actuation that produces the desired form of the flow is found iteratively and thus is computationally costly. Many examples of iterative algorithms can be found in the literature. The intent of this work is to demonstrate that a direct determination of the actuation is possible, i.e., we specify the desired flow property and determine the required actuation directly.
Back to top

--------------

Ian A. Frigaard, University of British Columbia
Coauthors: Kamran Alba, Seyed Mohammad Taghavi
A Weighted Residual Method for 2-Layer Flows with Yield Stress Fluids

Buoyancy dominated displacement flows are important in many industrial processes. In operations such as oilfield cementing, fracturing and drilling the fluids involved are non-Newtonian. An industrially relevant regime is that in which weak inertial effects are present. Density differences often lead to stratification during displacement and potentially to instability/mixing. An appropriate model for this type of flow is a lubrication/thin-film displacement model, which models the evolving stratification. However, the neglect of inertial effects in such models limits their applicability.

Rather than use 2D or 3D simulation for these flows, which is particularly costly for yield stress fluids, it is of interest to model these flows using reduced models. On the other hand, we would like to predict the stability and displacement characteristics of the flow. Here we present our current work on modelling these flows. A recent approach to modelling weak inertial effects is the weighted residual method of Ruyer-Quil Manneville [1]. This has been extended to two-layer Newtonian channel flows by Amaouche et al. [2]. The basic approach gives a 2nd order accurate approximation to the interface height and volumetric fluxes, while reducing the model complexity to two coupled 1D conservation laws, and also reproducing the (long-wavelength) stability characteristics of the 2D flow. We show how this approach is extended to two-layer flows in which both fluids are of Herschel-Bulkley type. Although the derivation is complex, the resulting equations have the same structure as the Newtonian fluid model. We present examples from the analysis of these equations and discuss possible generalisations.
References
[1] C. Ruyer-Quil and P. Manneville, Improved modeling of flows down inclined planes, Eur. Phys. J., B 15, (2000) 357-369.
[2] M. Amaouche, N. Mehidi, and N. Amatousse, Linear stability of a two-layer film flow down an inclined channel: A second-order weighted residual approach. Phys. Fluids 19 (2007) 084106.1-084106.14.
Back to top

----------------
Alex Hay, Department of Oceanography, Dalhousie University
On the Dynamic Interactions between Turbulent Oscillatory Boundary Layers and Mobile Sediment Beds

Using as a basis results from experiments carried out both in the real ocean and in the laboratory, including measurements with a new multi-frequency Doppler profiler developed in collaboration with Len Zedel at Memorial University, the interactions among wave and current forcing over beds of mobile sediment, the different patterns of mobile bed adjustment, and the vertical and temporal structure of flow and turbulence in the wave bottom boundary layer, are presented and discussed. The purpose of the talk is to indicate that the field of mobile bed dynamics in near-shore and continental shelf environments is entering a transformative stage, one in which the measurement tools have advanced to the point that meaningful comparisons between observations and numerical simulations are within reach.

----------------

Tiger Jeans, University of New Brunswick
Analysis of a Lift Based Ocean Wave Energy Converter using Unsteady Reynolds Average Navier-Stokes Simulations

The viscous wave generation properties of a novel lift based wave energy converter, namely, a Cycloidal turbine, are investigated. The energy converter consists of two hydrofoils attached parallel to a horizontal main shaft at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The local flow field induced by the incident wave will cause the hydrofoils to rotate about the main shaft. The orientation of each hydrofoil is adjusted to produce the desired level of bound circulation. Previous two-dimensional potential flow simulations demonstrated 99% and 77% wave cancellation in straight crested regular and irregular deep ocean waves, respectively. Here the unsteady RANS equations are employed to extend the analysis to include nonlinear viscous effects. Free surface capturing is achieved using the volume of fluid method. CFD results are validated against 1/10 scale model experiments and potential flow simulations. Resulting surface waves, hydrofoil bound circulation, and shaft torque are determined for fixed angles of incidence.
Back to top

----------------

Sarah Hormozi
Department of Mathematics, University of British Columbia
Coauthors: I.A. Frigaard & N.J. Balmforth
A mathematical model to predict the shape of thickened tailings

Surface deposition of mine tailings with high water content entails not only the risk of catastrophic failure and environmental damage but is also waste of water resources. Therefore, thickened tailings deposition is a fast growing technology in both the mining and oil sands industries. Prediction of the tailings profile is essential in calculating the storage capacity and designing the thickening process. However, this prediction is a challenging problem due to complex rheology of thickened tailings and the role of a wide range of mechanisms such as sedimentation, consolidation, desiccation (evaporation), etc. Existing models poorly predict the shape of tailings disposal.
We present preliminary results of a mathematical model to predict the shape of thickened tailings. Thickened tailings are modelled as a viscoplastic fluid containing coarser solid particles. The system of fluid and solid particles is modelled as a single phase using a mixture model with Herschel-Bulkley constitutive law, but modified to include the effect of solid volume fraction on viscosity and yield stress. A thin-layer theory is developed to explore the effects of sedimentation, consolidation and yield stress on the spreading dynamics of the thickened tailings.
Back to top

-------------

Hossein Amini Kafiabad
Mechanical Engineering, McGill University
Coauthors: George Haller and P. W. Chan
Lagrangian Detection of Aerial Turbulence for Landing Aircraft

Recent studies have shown that aerial disturbances affecting landing aircraft have a coherent signature in the Lagrangian particle dynamics inferred from Light Detection And Ranging (lidar) velocity scans. Specifically, attracting Lagrangian Coherent Structures (LCSs) mark the intersection of localized material upwelling with the cone of the lidar scan. Here we test the detecting power of LCSs on historical landing data and corresponding pilot reports of disturbances from Hong Kong International Airport (HKIA). We find that a specific LCS indicator, the gradient of the Finite-Time Lyapunov Exponent (FTLE) field along the landing path, provides an efficient marker of turbulent upwellings. In particular, Receiver Operating Characteristics (ROC) graphs show that projected FTLE gradients approach the efficiency of the wind shear alert system currently in operation at HKIA, even though the latter relies on multiple sources of data beyond those used in this study.
Back to top
----------------

(C) P.N.Kaloni, Dept. of Mathematics and statistics University of Windsor
Magnetic Fluids: A critical study of the Constitutive Equations

Magnetic flids are stable colloidal suspensions of fine ferromagnetic mono domain nanoparticles in a non-conducting carrier fluid.These fluids have found several industrial applications in cooling and damping of loud speakers,in shock absorbers in jet printing and in biomedical applications,such as
drug targeting.These fluids are different from the fluids which are dispersions of micon sized particles,and in which the main interest is related to the non-Newtonian propertiesvery much like in polymer fluids. In the recent years a variety of constitutive equations have been proposed to describe these fluid.Some of these are phenomenological,some are based on thermodynamics,some of these are based upon the internal rotation of the particle,some are based on the statistical mechanics consideration,and some are based upon the dynamic mean-field theory. There are very few experimental results available,and thus the predictions based upon the different theories can not be properly described and discussed. Our purpose here is to first discuss critically the developmement of these equations and then solve a bechmark problem in all theories,for which,if not complete,some experimental information is available.
Back to top

---------
Ida Karimfazli, University of British Columbia
Coauthors: I. A. Frigaard
On the natural convection of stratified Bingham fluid in a vertical channel with differentially heated side walls

Vertical ducts filled with yield stress fluids and with differentially heated walls are found in the drilling and cementing of oil wells, as well as potentially in other construction geometries and geophysical contexts. In these settings it is of interest to determine whether or not the thermal heating effects are sufficient to promote fluid motion.
As an archetypical flow we consider a vertical plane channel flow between two differentially heated walls, separated by a distance L. In addition to a constant temperature difference, there is a linear vertical temperature variation imposed at the walls. This configuration was studied by Bergholz(1978) in the case of Newtonian fluids. The base flow is governed by two dimensionless parameters: a stratification parameter and a Bingham number. Of academic interest is the fact that for sufficiently large stratification parameter and small Bingham number it appears we can find infinitely many unyielded plug regions - a peculiarity for a steady flow in a finite domain.
We present an analysis of onset of flow and a classification of base flow at various stratification parameter and Bingham numbers.
Back to top
----------------

Richard Karsten, Acadia University
Analysis of Tidal Turbine Arrays in the Digby Neck Passages
Coauthors: Mitchell O'Flaherty-Sproul, Joel Culina, Justine McMillan, Greg Trowse, Alex Hay

The Nova Scotia government has approved tidal power Community-Feed-in-Tariffs for two passages along Digby Neck--Digby Gut and Petit Passage. Digby Gut is a passage connecting the small, enclosed Annapolis Basin to the Bay of Fundy. It has tidal currents up to 3 m/s. On the other hand, Petit Passage is a passage between the large, open St. Mary's Bay and the Bay of Fundy. It has strong tidal currents that can exceed 5 m/s. The critical difference is that altering the flow in Digby Gut strongly affects the surrounding tides, while altering the flow in Petit Passage does not. Thus, while the passages have a similar size and volume flux, the theoretical maximum extractable power for Digby Gut is over 200 MW but for Petit Passage is only 40 MW! Using validated, high resolution, 3D numerical models of the tides and tidal currents through the passages, we examine the power generation potential of turbine arrays in these two passages and calculate the impact that power extraction will have on the currents and tides. Finally, we examine how arrays of in-stream turbines should be designed for each passage based on their geometry and tidal dynamics.
Back to top

----------------
(Talk Cancelled) Brendan Keith, Department of Mathematics and Statistics, McGill University
Coauthors: Hossein Amini Kafiabad (Department of Mechanical Engineering, McGill University)
Nonlinear dynamics and chaotic motion of a non-spherical single bubble surrounded by viscoelastic fluid

We study nonlinear dynamics of a non-spherical, acoustically driven gas bubble surrounded by a viscoelastic fluid. The Maxwell fluid is picked as the model for the surrounding liquid to include the simultaneous effects of viscosity and elasticity. For our model, we derive the governing equations of motion by perturbing the spherical configuration of the bubble in terms of the spherical harmonic modes. In this, a robust numerical approach enables us to capture the bubble behavior in very high amplitudes of excitation. The stability of spherical modes as well as their bifuractions are then studied by changing physical parameters such as Debora number, Reynolds number, and amplitude and frequency of excitation. Moreover, the onset and characteristics of chaos in the bubble dynamics are investigated in our analysis. Our results show that some important impacts of rheology on the bubble behavior can only be revealed by taking the nonsphericalities into account.
Back to top

----------------

Boualem Khouider, University of Victoria
Convective momentum transport and multiscale organization of convectively coupled tropical waves

Convection in the tropics is organized into a hierarchy of scales ranging from the convective cells of 1 to 10 km, to mesoscale cloud clusters of 100 to 500 km, to synoptic scale waves of 1000 to 5000 km to to planetary scale waves of 10,000 to 20,000 km. The atmospheric planetary scale variability, in winds and precipitation, is dominated by an intra-seasonal oscillation of 40 to 60 days known as the Madden-Julian oscillation (MJO) while convectively coupled Kelvin waves (CCKWs) dominate the synoptic scale variability. The MJO disturbance starts in the Indian ocean warm pool as a standing wave and slowly propagates eastward at roughly 5 m/s. The MJO has a significant impact on weather and climate patterns and extremes in the tropics and extra-tropics yet contemporary global climate models (GCMs) simulate poorly the MJO and organized convective systems in general. CCKWs are trapped in the vicinity of the equator and move eastward at 15 m/s. Multiscale CCWs are often embedded in each other like Russian dolls; The MJO often appears as an envelope of synoptic and mesoscale waves and mesoscale waves often develop inside Kelvin waves. The complex interactions across scales associated with this multiscale organization remain poorly understood and misrepresented in climate models.

Convective clouds not only release heat and moisture into the troposphere but they also deposit momentum due to the underlying eddies. This latter phenomenon known as convective momentum transport (CMT), applies also to turbulent fluxes associated with mesoscale and synoptic scale convective organized systems when regarded from larger scales. However, while the small eddies, associated with parcel lifting, result essentially in large-scale momentum damping, a.k.a cumulus friction, due to their chaotic nature just like the usual fluid dynamics turbulence, there is enough observational, numerical, and theoretical evidence that the CMT associated with meso- and synoptic-scale convective systems can significantly accelerate and/or decelerate the ambient flow. In this talk, we present some numerical simulations of CCKWs, in a channel domain, using the WRF model that shows evidence of coherent CMT fluxes from mesoscale convective systems embedded within the large scale Kevin wave. We then propose a simple model parametrization that takes into account the effect of CMT from unresolved mesoscale convective systems in GCMs. It is demonstrated, in the context of a toy GCM, that mesoscale CMT helps the organization of and strengthens substantially the planetary and synoptic scale waves, i.e., the MJO and Kelvin waves.
Back to top

----------------

Mary Catherine Kropinski (SFU)
Coauthors: Nilima Nigam
Fast Integral Equation Methods for the Laplace-Beltrami Equation on the Sphere

Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a stereographic projection. After discretizing the integral equation, the resulting dense linear system is solved iteratively using the fast multipole method for the 2D Coulomb potential in order to calculate the matrix-vector products. This numerical scheme requires only O(N) operations, where N is the number of nodes in the discretization of the boundary. The performance of the method is demonstrated on several examples, including the motion of several point vortices on the sphere.
Back to top

------------------
Michael Lindstrom, Brian Wetton, [A third author may be added
Modelling Nuclear Fusion Reactors: Numerical Approximations of Fluid Dynamics Equations inside a Moving Domain

A modern engineering design for harvesting nuclear energy involves the implosion of a sphere of liquid lead with hydrogen plasma filling its central axis. The intense pressure generated by the imploding lead is aimed at fusing the plasma, releasing energy. The mathematical modeling of such an apparatus involves a careful interplay between fluid dynamics and plasma physics, along with suitable numerical approximation schemes for nonlinear hyperbolic PDEs with moving boundaries. Our work begins with a simplified one-dimensional model with a moving interface at the left and right, within which there is liquid lead. This talk will present our current work, where a low-order numerical scheme for hyperbolic PDEs is used to couple mass and momentum conservation, the lead equation of state and elementary plasma properties, in order to predict the compression of the plasma. In the process, we also investigate the optimal implementation of the boundary conditions.
Back to top

--------------
Frances Mackay, Colin Denniston
The University of Western Ontario
Liquid Crystal Induced Colloidal Deformation

We numerically investigate the behavior of 2D deformable particles immersed in a liquid crystal. A bead-spring model is used to represent the particles, while the liquid crystal is modeled using the lattice-Boltzmann method. Perpendicular anchoring is assumed at the particle surface, leading to distortions in the bulk liquid crystal orientation. These distortions result in non-spherically symmetric local forces acting on the elastic particle membrane, causing a deformation of the particle. We present the resulting particle shapes for a range of surface elasticities, and investigate the interaction between pairs of particles.

Peter Minev, University of Alberta
Coauthors: Jean-Luc Guermond
Massively-parallel direction splitting techniques for the incompressible Navier-Stokes equations with a variable density and viscosity

A new direction-splitting-based fractional time stepping for solving the incompressible Navier-Stokes equations will be discussed. The main originality of the method is that the pressure correction is computed by solving a sequence of one one-dimensional elliptic problem in each spatial direction. The method is unconditionally stable, very simple to implement in parallel, very fast, and has exactly the same convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. The one-dimensional problems are discretized using central difference schemes which yield tri-diagonal systems. However, other more accurate discretizations can be applied as well. The scheme is further extended to allow for the computation of flows with non-constant density/viscosity without the need to recompute the matrix and its Schur complement at each time step. This is achieved via a perturbation of explicit schemes which stabilizes them in the spirit of the direction splitting schemes discussed above.
Back to top
----------------

James Munroe, Memorial University of Newfoundland
Coauthors: Sylvain Joubaud, Philippe Odier, Thierry Dauxois
Measuring Parametric Subharmonic Instability in Internal Waves

Parametric subharmonic instability is a mechanism of energy transfer between internal waves from large to small spatial scales. In this type of resonant triad interaction, a parent wave of higher frequency destabilizes leading to the growth of two daughter waves with lower frequencies. In a laboratory experiment, a full-depth wave generator forces a high frequency vertical mode-1 internal wave and parametric subharmonic instability is observed. The growth rate of the instability is measured using a time-frequency analysis and compared with theoretical predictions.
Back to top

----------------
(C)Lidia Nikitina, Carleton University, School of Mathematics and Statistics
Coauthors: Lucy Campbell
Propagation of Rossby waves in a tropical cyclone

Observational analyses of hurricanes in the tropical atmosphere indicate the existence of spiral rainbands which propagate outwards from the eye and affect the structure and intensity of the hurricane. These disturbances may be described as vortex Rossby waves. Under certain conditions, two concentric rings of high-intensity wind (concentric eyewalls) develop. The outer or secondary eyewall appears to be related to wave-mean-flow interactions near the critical radius where the mean flow angular velocity matches the phase speed of the waves. In this study we carry out asymptotic analyses to examine the evolution of the interactions near the critical radius in some two-dimensional configurations on an f-plane and a beta-plane.

----------------

(C) Mohammad Niknami, Department of Mechanical and Materials Engineering , Western University
Coauthors: Roger Khayat

The stability of natural convection in a non-Fourier fluid layer between two parallel vertical plates is investigated theoretically. The two plates are maintained at different constant temperatures and their length is assumed to be tall enough so they can be regarded as infinite length in the vertical direction. Single-Phase-Lag heat conduction relation is used for the heat equation, in an attempt to model the convection of non-Fourier fluids. This means that the traditional Fourier law of heat conduction is not applicable here anymore. Unlike the horizontal fluid layer flow (Rayleigh-Benard convection), vertical motion in the base flow in the vertical slot case will affect the critical conditions for the onset of secondary convection. The critical Grashof number for instability to occur is obtained in the case of some different Prandtl and Cattaneo numbers.
Back to top

----------------

Robert G. Owens, Département de mathématiques et de statistique, Université de Montréal
Coauthors: Yasmine Tawfik
Oscillations in realistic models of large capillary networks: physical or numerical?

Fluctuations in red cell velocities and concentrations observed in capillary networks have traditionally been ascribed to biological control (precapillary sphincters, vasomotion) and statistical variations in cell and vessel properties (Fung (1973)). However, it is now believed that hemorheological factors in the network may also influence temporal variations in the flow parameters. The development of mathematical models of the microvasculature has allowed the dynamics in large networks to be studied in the absence of biological control. Are fluctuations in flow parameters in such models physical, an artefact of an unrealistic model or are they (at least in part) numerical?
Although it has been proved mathematically in the case of small networks and a simple model of microvascular blood flow that Hopf bifurcations of the equilibrium solution can occur (see, for example, Geddes et al. (2007)), the situation for more realistic (and therefore more complicated) models and large networks is less clear and no consideration seems to have been given to the role that the choice of numerical algorithm employed may play in the observed results. Since the pioneering paper of Schmid-Schönbein et al. (1980), the Picard-type numerical algorithm adopted by many authors for solving blood flow in the microcirculation has been to solve alternately at each time step a linear problem for the nodal pressures and a non-linear problem for the determination of the segment hematocrits and apparent viscosities (see, for example, Pries et al. (1990), Kiani et al. (1993, 1994), Obrist et al. (2010)). Kiani et al. (1993, 1994) reported the appearance of oscillations in flow parameters that apparently were caused by hemodynamic factors at network bifurcations alone, and not due to fluctuating boundary conditions, vasomotion or other forms of biological control.
In this talk we will study blood flow through large microculatory networks using the model of Pries et al. (1990) and two different numerical algorithms. The first is the traditional Picard-type method mentioned already and the other is a new iterative scheme that allows us to solve the linear and non-linear parts of the problem together in an efficient manner. This is done using a quasi-Newton method for the outer iterations and preconditioned conjugate gradient and GMRES methods for the inner iterations. We compare the results of the two approaches in order to ascertain to what extent the oscillations that have been observed using the traditional scheme may be attributable to this choice of numerical method.
Back to top

----------------

Dominique Pelletier (Ecole Polytechnique Montreal)
Coauthors: Stephane Etienne
Verification of codes and simulations for unsteady incompressible flows on deforming domains

We discuss the method of manufactured solution (MMS) for code verification of incompressible flows on deforming domains ( free surface flows, fluid structure-interactions, and fluid rigid solid interaction). MMS provides closed form solutions to the flow PDEs so that the error can be computed and it convergence monitored by grid and time-step refinement studies. Techniques are described for high order implicit Runge-Kutta time integrators.
----------------

Nicolas Perinet, University of Ontario Institute of Technology
Coauthors: Gregory M. Lewis, Lennaert van Veen
Secondary Transitions and Instabilities in Geophysical Fluids

We track invariant solutions in a model of the differentially-heated rotating annulus, an experiment that presents analogies with atmospheric circulation. The rotation rate of the annulus is of fundamental importance. Indeed, low rotation rates generate steady flows similar to those observed in the tropical atmosphere. An increase in the rotation rate causes these stationary solutions to bifurcate to periodic solutions taking the form of travelling waves. A secondary bifurcation leads to quasi-periodic flows such as mixed-mode or amplitude-vacillating flows, which are similar to the atmospheric flows of temperate regions. The study involves numerical continuation methods in a flow modeled by the three-dimensional Navier-Stokes equations in the Boussinesq approximation.
Back to top

----------------

Francis Poulin, University of Waterloo
Coauthors: Guillaume Lapeyre, Laboratoire de Météorologie Dynamique
Exploring Vortex Asymmetry in a Simplified Two-Level QG+1 Model

Quasi-Geostrophy (QG) has played a pivotal role in exposing the underlying dynamics of the large-scale Atmosphere and Oceans. Even today where so much research is numerically based, QG is still very popular because of how efficient it is in describing motions dominated by rotation. Over a decade ago a next-order correction to QG, aptly named QG+1, was derived that allowed for some non-QG effects while still remaining very simple compared to the primitive equation models. Here, we present a reduced version of QG+1 that only has two vertical levels. This includes one barotropic and one baroclinic mode that can exhibit vortex asymmetry. By studying the dynamical balances we determine the mechanisms that can achieve either a dominance of cyclones or anticyclones and demonstrate this through numerical simulations of freely-evolving turbulence.
Back to top
----------------

Bartosz Protas, McMaster University
Coauthors: Diego Ayala (McMaster University)
Maximum Palinstrophy Growth in 2D Incompressible Flows

This investigation is a part of a broader research effort seeking to construct solutions of the Navier-Stokes system in 2D and 3D which can saturate certain analytically obtained bounds on the maximum growth of enstrophy and palinstrophy. This research is motivated by questions concerning the possibility of finite-time blow-up of solutions of the 3D Navier-Stokes system where such estimates play a key role. We will argue that insights concerning the sharpness of such estimates can be obtained from the numerical solution of suitably-defined PDE optimization problems. Following a review of the available analytical estimates for the maximum instantaneous and finite-time growth of palinstrophy in 2D flows, we will present computational results concerning realizability of such growth in actual flows.
Back to top
--------------

(C) Bryan Quaife, University of Texas
Coauthors: George Biros (University of Texas)
Boundary Integral Methods for Inextensible Vesicle Dynamics in 2D

A boundary integral method for simulating inextensible vesicles in a 2D viscous fluid was developed by Veerapaneni et. al. Recent extensions include developing preconditioners, implementing a near-singular integration strategy, and allowing for vesicles with different bending moduli. The goal is to run simulations with a high concentration of red blood cells and platelets.
Back to top

--------------

(C) A. Roustaei UBC Mechanical Engineering Department
Coauthors: I.A. Frigaard
Onset of fouling in channels with uneven walls

We consider the pressure driven flow of a Bingham fluid along a channel with uneven walls. We are interested in the situation where the fluid gets stuck to the wall of the channel in the widest part. This could be a typical flow that occurs in many industrial applications related to oil and gas wells, e.g. drilling and cementing. In industries such as food processing, such residual deposits represent a health hazard. We represent the channel wall by a sinusoidal variation. The Stokes problem is solved numerically a finite element based discretization and the augmented Lagrangian method. As the (channel wall) wave amplitude increases, a static zone appears on the widest section of the channel. We study the formation of this static zone and it's dependence on a wide range of the three dimensionless parameters of the problem: the Bingham number, channel aspect ratio and wave amplitude. We observe some interesting features in the flow pattern and velocity field, e.g. the final flow geometry of two different channels can be quite similar when the static zone exists. Also some accelerating flow regions are found in the diverging part of the channel, which is counter intuitive.We outline our attempts at predicting some of these features analytically.
Back to top

---------------

(C) Amir Sayed, Carleton University
Coauthors: Lucy Campbell (Carleton University)
Generation of Internal Gravity Waves by Convection in the Atmosphere

Internal gravity waves affect the general circulation of the atmosphere and hence it is important to understand their generation, propagation and interactions in order to represent them correctly in weather prediction and climate models. The primary mechanisms for gravity wave generation are convection in the lower atmosphere and topography; however, the mechanisms for convective generation are not fully understood. In this study we develop a two-layer model of internal gravity waves over convective vortices and use weakly-nonlinear analyses and numerical simulations to obtain approximate solutions and investigate some of the current hypotheses for convective generation mechanisms.
Back to top

--------------
Samuel Shen, San Diego State University
Uncertainties, Trends, and Hottest and Coldest Years of US Surface Air Temperature Since 1895

This lecture discusses the sampling error variances of gridded monthly US Historical Climatology Network Version 2 (USHCN V2) time-of-observation bias (TOB) adjusted data. Our analysis of mean surface air temperature (SAT) assesses uncertainties, trends, and the rankings of the hottest and coldest years for the contiguous United States in the period of 1895-2008. Data from the USHCN network stations are aggregated onto a latitude-longitude grid by an arithmetic mean of the stations inside a grid box. The sampling error variances are smaller (mostly less than 0.2 (degrees celcius)x2 over the eastern US where the station density is greater, and larger (with values of 1.3 (degrees celcius)x2 for some grid boxes in the earlier period) over mountain and coastal areas. In the period of 1895-2008, every month from January to December has a positive linear trend. February has the largest trend of 0.162 degrees celcius /decade, and September has the smallest at 0.020 degrees celcius/decade. The three hottest (coldest) years measured by the mean SAT over the US were ranked as 1998, 2006, and 1934 (1917, 1895, and 1912).
Back to top

--------------

Raymond Spiteri, Computer Science, University of Saskatchewan
Coauthors: Ahmed Kaffel
Modeling and numerical simulation of particulate flows in fluidized beds

Gas-solid fluidized beds are widely used in the chemical, petroleum and energy industries. For instance, fluid catalytic cracking which is the process of almost every oil refinery, consists of fluidized beds on the order of meters. At present, the design and scale-up of such fluidized bed reactors are mostly fully empirical processes, owing to limited insight into the fundamentals of gas-solid flows at different scales. In particular, the collisions forces, drag forces, dissipation, and solid-wall interactions are not well understood. For this reason, many preliminary tests on pilot-scale model reactors have to be performed, which is a time-consuming and expensive activity. To aid this design process, computer simulations can clearly be a useful tool. However, a major difficulty in modeling life-size fluidized beds is the large separation of scales where the largest flow structures are on the order of meters but depend on the solid-solid and solid-gas interactions that take place on the order of millimeters or even micrometers. To describe the time evolution of both phases and predict the flow behavior of gas-solids flows of systems at large scales, we study issues of modeling and simulation of particulate flows in fluidized beds and compare with available experimental data.
A mathematical model for two-phase gas particle flow in a fluidized bed is developed from the basic principles of conservation of mass and momentum. It consists of a set of partial differential equations with coupling and interaction between the two phases and assumes incompressibility in both solid and gas phases, with equal particle diameters. Numerically, we solve the fluid phase continuity and momentum equations following an Eulerian approach and the particle motion following a Lagrangian approach. We show that the flow structure and its evolution in various flow regimes can be reproduced from these numerical simulations by including the competition between particle collisions and particle-fluid interaction.
Back to top

----------------

Marek Stastna, University of Waterloo
The effects of the Earth's rotation on large amplitude internal waves

The effects of the Earth's rotation on linear waves in a continuously stratified fluid have been known for many decades. The central result is the lower bound on frequency which implies that the phase speed of rotation modified waves is potentially unbounded (even though the more physically grounded group speed remains bounded). Recent studies have led to a developing understanding of how the linear results carry over to internal solitary waves. I will review the published results, showing examples of the phenomenon of overtaking solitary waves, as well as more chaotic phenomena. I will subsequently discuss more recent work on the generation of waves over topography by supercritical flow that leads to the astonishing prediction that in the presence of rotation, supercritical flow over topography in the coastal ocean can lead to the generation waves with an amplitude in excess of 40 meters (in water 100 meters deep) at a distance of 100 kilometres from the obstacle.
Back to top

----------------

Catherine Sulem, University of Toronto
Coauthors: Walter Craig and Philippe Guyenne
Coupling between internal and surface waves in a two-layers fluid Un

Internal waves occur within a fluid that is stratified by temperature or salinity variation. They are commonly generated in the oceans, and large amplitude, long wavelength nonlinear waves can be produced in the interface and propagate over large distances. In some physically realistic situations, the visible signature of internal waves on the surface of the ocean is a band of roughness, sometimes referred to as a ‘rip’ which propagates at the same velocity as the internal wave, followed after its passage, by the ‘mill pond’ effect, the complete calmness of the sea. We propose an asymptotic analysis of the coupling between the interface and the free surface of a two layers fluid in a scaling regime chosen to capture these observations. In particular, we describe the rip region of the free surface as being generated by the resonant coupling between internal solitons and the free-surface wave mode. We also give an explanation of the mill pond effect as the result of a strong reflection coefficient for free-surface waves in the modulational regime, in a frame of reference moving with the internal soliton.
Back to top

----------------
Yu-Hau Tseng, York University
Coauthors: Kuo-Long Pan, Ming-Chih Lai
Immersed Boundary Method for Head-on Droplets Collision and Phagocytosis with Surfactant

A numerical method based on the immersed boundary method is proposed to simulate the collision between two identical water droplets mixed with surfactant. In dynamics of water droplets collision, the bouncing phenomenon was not observed for pure water in the atmosphere, but was found for water droplets with surfactant in experiments. In relevant literatures, this regime was conjectured to be caused by the nonuniform distribution of surfactant and hence the gradient of its concentration near the droplet surface, known as Marangoni effect. This could substantially affect the fluid motion by varying such critical mechanisms as the interfacial deformation of liquid and draining dynamics of gas intervening between the interfaces. Innumerical experiments, a numerical method to handle the solubility of the surfactant in the
droplets is verified, a series of numerical tests with consideration of intermolecular forces are compared to underline the dominance of the Maragoni effect, and numerical results produced by
different amount of surfactant are presented. In second part, phagocytosis is one of endocytosis functions which captures vesicles or microorganism into a cell. In phagocytosis, several kinds of surfactant coexist and chemical reaction among these surfactant derives a great diversity of interface dynamics. A simple mathematical model and corresponding numerical method for
phagocytosis, and the preliminary results will be presented.
Back to top

----------------

José Urquiza (GIREF, département de mathématiques et de statistique, Université Laval )
Coauthors: Bocar Wane and André Fortin
Anisotropic mesh adaptation and iterative methods for free surface turbulent flows.

We show how iterative methods based on the hierarchical quadratic finite elements and an anisotropic mesh adaptation strategy can be used to solve efficiently free surface turbulent flow problems. For the turbulence modeling, a logarithmic formulation of the k-epsilon model is used, and the free surface is computed using the level set method.The whole strategy is applied to various problems ranging from a simple manufactured solution to 3D flows around obstacles piercing the free surface.
Back to top

----------------
Henry van Roessel, University of Alberta
Two species coagulation-annihilation

The irreversible growth of a species of particles by the successive merger of clusters of particles occurs in many fields of science, such as polymer chemistry, colloid science, cloud dynamics and star formation. The most popular mean-field model describing such phenomena is Smoluchowski's coagulation equation.
Now consider the situation of two distinct species, where two clusters of the same species will merge or coalesce when they come together, but where clusters of different species will be annihilated when they come together. This situation can be modelled by a generalized form of Smoluchowski's coagulation equation.mThe long time behaviour of this scenario will be discussed.
Back to top

--------------
Lennaert van Veen, University of Ontario Institute of Technology
Coauthors: Genta Kawahara, Osaka University, Japan.
The onset of sustained turbulence in channel flow

The motion of a fluid trapped between two parallel, moving walls, otherwise known as Couette flow, is known to be laminar at small forcing and turbulent at large forcing. However, the laminar state is a dynamically stable equilibrium at all Reynolds numbers. There is no generally accepted theory for the transition to turbulence in the presence of a stable laminar state. In this presentation I will review some proposed theories, focussing on the ëdge state" hypothesis and in particular on the recent discovery of solutions homoclinic to edge states. Such solutions might explain irregular turbulent bursting near the transition threshold and help us define a critical Reynolds number.
Back to top

----------------
Mike Waite (Waterloo)
Buoyancy scale dynamics in direct numerical simulations of stratified turbulence

New direct numerical simulations (DNS) of strongly stratified turbulence will be discussed. Stratified turbulence presents a particular computational challenge, because stable stratification tends to reduce the characteristic vertical scale of the turbulence. As a result, as the Froude number of a flow is reduced, higher Reynolds numbers are necessary to obtain a turbulent cascade. The classical picture of such flows is that there is a transition from stratified to isotropic turbulence below the Ozmidov scale. However, recent simulations with ad hoc small-scale dissipation have shown that a transition occurs at the (larger) buoyancy scale U/N, where U is the r.m.s. velocity and N is the buoyancy frequency. Here, I will show that these transitions are also present in DNS, even at relatively modest Reynolds numbers. They appear to result from Kelvin-Helmholtz instability of the large-scale quasi-horizontal flow, and corresponds to a direct, non-local transfer of energy from large to small scales.
Back to top

----------------

Jonathan Wylie (City University of Hong Kong)
Coauthors: Huaxiong Huang and Robert Miura
Asymptotic Analysis of a Viscous Drop Falling Under Gravity

Despite extensive research on extensional flows, there is no complete explanation of why highly viscous fluids falling under gravity can form such persistent and stable filaments. We therefore investigate the motion of a slender axisymmetric viscous drop that is supported at its top by a fixed horizontal surface and extends downward under gravity. We consider the full initial-boundary-value problem for arbitrary initial shape of the drop in the case in which inertia and surface tension are initially negligible. We show that, eventually, the accelerations in the thread become sufficiently large that the inertial terms become important. We therefore keep the inertial terms and obtain asymptotic solutions forthe full initial-boundary-value problem. The asymptotic procedure requires a number of novel techniques and the resulting solutions exhibit surprisingly rich behavior. The solution allows us to understand the mechanics that underlies highly persistent filaments.

Back to top

----------------
Xiaohua Wu,Royal Military College of Canada
Coauthors: Parviz Moin, Stanford University
Visualization of flat-plate boundary layer bypass transition with continuous freestream turbulence

We introduce the concepts of bypass transition in the narrow sense, and bypass transition in the general sense. A database with sufficient spatial information and reasonable temporal information has been created using very-large-scale direct numerical simulation on an incompressible, smooth flat-plate boundary layer with mild continuous freestream turbulence. Inlet freestream turbulence intensity is 3 percent, and decays with distance according to the -1/2 power-law to 0.8 percent by the exit station of momentum thickness Reynolds number 2000. Statistics in the transitional region are compared with those from previous bypass transition experiments and from theory. The evaluation demonstrates that the present transitional regime is a representative bypass transition in the narrow sense. Visualization of the bypass transition process indicates that the transition mechanism under mild continuous freestream turbulence bears good similarity with the secondary instabilities of natural transition as discussed in Klebanoff, Tidstrom, Sargent (1962), Herbert (1988), Bake, Meyer, Rist (2002). Specifically, quasi-spanwise structures arise inside the boundary layer through receptivity. Some of these structures develop into Lambda vortices, which are subsequently stretched and detached into pairs of obliquely oriented quasi-streamwise leg vortices. Hairpin packet forms within the detached L vortex, and breakdown ensues with the emergence of infant turbulent spot, which in itself is the hairpin packet with chaotic fluctuations. This process differs from the streak growth, streak secondary instability, and streak breakdown scenario reported in many previous bypass transition studies. The present mechanism is consistent with our previous work on boundary layer with discrete patches of freestream turbulence. It is therefore quite possible that boundary layer bypass transition, at least a subcategory of it, might be loosely treated, and probably modeled, as the secondary instability of natural transition with merely the TS-wave being circumvented. Razvan Fetecau,Simon Fraser University
Back to top

----------------
David Zingg
University of Toronto Institute for Aerospace Studies
Coauthors: David Del Rey Fernandez, Hugo Gagnon
Recent Progress in Computational Aerodynamics for Future Aircraft Design

This talk will present some recent progress in computational aerodynamics, including aerodynamic shape optimization. Topics to be discussed will include summation-by-parts finite-difference operators, superconvergence, and dual consistency. Moreover, an approach is presented that combines gradient-based optimization with Sobol sequences to provide global optimization and a two-level free-form deformation technique is described that provides a geometry parameterization suitable for optimization of unconventional aircraft configurations.
Back to top

----------------------
POST-DOCS

--------------
Maurizio Ceseri, Simon Fraser University
Coauthors: John Stockie
Mathematical modeling of sap flow in maple trees

In early spring, sap in maples starts flowing in the vessels of the tree after being dormant for the whole winter. The flux onset is triggered after ambient temperature fluctuates around the freezing temperature for several days. When temperature is below the freezing point of sap, ice starts forming in the interior wall of the air filled fibers of the tree drawing sap from the adjacent vessels. The ice compresses the air bubble into the fiber as it grows. Once ambient temperature rises above the freezing point, the above mechanism is reversed. We present here a compartment model describing the process for a single fiber and a vessel element.
Back to top

George M Homsy,University of British Columbia
Coauthors: Harish N Dixit
Cylinders on flat and curved interfaces: role of surface tension

We consider cylindrical particles floating on a fluid interface and investigate the role of surface tension in generating lateral forces on the particles. A single particle on a flat interface assumes a static equilibrium such that the weight of the particle is balanced by surface tension and buoyancy forces. But in the presence of a background curvature, the particle experiences unbalanced lateral forces. In the absence of gravity, the lateral force varies as the gradient of curvature of the background interface. To account for gravity, we employ a systematic perturbation procedure in B1/2, where B is the Bond number, to obtain analytical formulae for lateral force on a single particle. We then extend the analysis to obtain capillary attraction forces in the presence of multiple particles. Our procedure recovers the well known Nicolson approximation at leading order for attraction between two particles. Finally, we obtain the capillary forces for an infinite array of cylinders. This case will be shown to be distinct from the two cylinders case where we show that using a simple superposition approximation, as has often been done in literature, may lead to incorrect results. We will also describe one application of particles on an interface: dip-coating flow of a particle-laden films.
--------------

(C)Driss Yakoubi, GIREF, Universite Laval
Coauthors: A. Fortin, J. Urquiza, J. Deteix, E. Chamberland
A hierarchical iterative solver for the Navier-Stokes equations

We present in this work an iterative method for the solution of the incompressible Navier-Stokes equations. The method was first introduced in El maliki and Guenette [1]. A second order Taylor-Hood (P2-P1) element is used for the space discretization where the quadratic velocity is expressed using a hierarchical basis.
A second-order backward finite difference scheme is used for the time-derivative. The convection term is linearized using a second order extrapolation method. The overall method is therefore second order
in both space and time. The linear system at each time step takes some special form where the proposed iterative method exploits this decomposition and can be parallelized in a very efficient way. The method performs very well
even on anisotropic meshes presenting very elongated elements. The method is then applied to compute the three-dimensional flow in a stenosis and in a 2 to 1 sudden expansion. In both cases, we show that there is a symmetry breakup for steady solutions when the Reynolds number is increased.
References:
[1] A. El Maliki and R. Gu´enette. Efficient preconditioning techniques for finite-element quadratic discretization arising from linearized incompressible Navier–Stokes equations. International Journal for Numerical Methods in Fluids, 63(12):1394–1420, 2010.

Back to top