The ability to model fluid solid interaction such as fluid flow with particles with high accuracy is central to the improvement of many chemical processes (e.g. fluidized bed, slurry transport). Multiple techniques exist to numerically model these flows. These different approaches vary in their precision and the scale of the problem they can handle. Resolved computational fluid dynamics combined with a discrete element method (CFD-DEM) is able to predict the flow around a few particles without the need of a closure model. This makes this approach the perfect candidate to analyze the dynamics of a small cluster of particles in a fluid. Such simulation can then be used to generate a more accurate closure model for large-scale simulation approaches (e.g. unresolved CFD-DEM). The quality of the closure models depends on the precision of the simulations they are derived from. Recent development in the literature seems to demonstrate that high order schemes (convergence order higher than two) can reach higher precision results in less computational time, thus making the development of a high order CFD-DEM a good option to generate closure models [1]. Since resolved CFD-DEM requires the resolution of a moving boundary problem in an incompressible Navier-Stokes problem, it is key to be able to demonstrate that high order can be reached in this case.
In this presentation, we present the verification procedure of our resolved CFD-DEM solver. This solver uses the continuous Galerkin-least-square formulation of the incompressible Navier-Stokes equations for the fluid and discretizes the particles with a sharp interface immersed boundaries. This approach has been shown to be able to reach high order of convergence for non moving boundaries. To show that the same method can reach a high order of convergence in space for a moving boundary case, we use the method of manufactured solutions (MMS) based on the Stokes solution for the flow around a single particle. With this case, we demonstrate that this solver reaches high order convergence in space for the solution of the velocity field.

This is joint work with Stéphane Etienne, Cédric Béguin and Bruno Blais. This work supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the RGPIN-2020-04510 Discovery grant.

[1] B. Blais et al., “Lethe: An open-source parallel high-order adaptative cfd solver for incompressible flows,” SoftwareX, vol. 12, p. 100579, 2020.