Unsteady flow situations for which a boundary of the domain is deforming require specific attention from a numerical standpoint, especially for methods we develop which rely on a mesh to discretize the flow domain. The main criterion is to ensure that the order of convergence of the underlying numerical method is not affected by a non uniform motion of nodes. We will discuss of our experience in achieving such effective methods[1]. A mesh deforming technique has been set up to continuously accompany the deformation of boundaries. We selected a pseudo-solid approach which mimicks a continuous medium without inertia. When comes to the control of the error, especially for unsteady applications, one could rely on the ALE approach to adjust the location of nodes in a domain or remesh part of or the whole domain. We selected the remeshing approach. Adaptive remeshing and criteria for remeshing triggering are based on the Zhu-Zienkiewicz error estimator.

The ALE approach developed yields accurate solutions of mechanical vibrations of structures interacting with fluids. We discuss specific cases of rotational galloping of non-circular cylinders and fluidelastic instability of tube bundles in crossflow. The combined ALE and remeshing technique allowed to develop an interface tracking approach that by definition strictly sticks to the fluids interface. The methodology has been applied to breaking wave dynamics in tanks which generate involved boundary deformations induced by the Kelvin-Helmholtz instability and ensuing small scale vortices at the free-surface.

[1] Hay, A, Yu, KR, Etienne, S, Garon, A, and Pelletier, D (2014). High-order Temporal Accuracy for 3D Finite-element ALE Flow Simulations, Comput Fluids, 100, 204–217.