Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

Achievement of Global Second Order Mesh Convergence for Discontinuous Flows with Adapted Unstructured Meshes

In the context of steady CFD computations, some numerical experiments point out that only a global mesh convergence order of one is numerically reached on a sequence of uniformly refined meshes although the considered numerical scheme is second order. This is due to the presence of genuine discontinuities or sharp gradients in the modelled flow. In order to address this issue, a continuous mesh adaptation framework is proposed based on the metric notion. It relies on a L p control of the interpolation error for twice differentiable functions. This theory provides an optimal bound of the interpolation error involving the Hessian of the solution. From this estimate, an optimal metric is exhibited to govern the adapted mesh generation. As regards steady flow computations with discontinuities, a global second order mesh convergence should be obtained. To this end, a higher order smooth approximation of the solution is reconstructed providing an accurate and reliable Hessian evaluation. Several numerical examples in two and three dimensions illustrate that the global convergence order is recovered using this mesh adaptation strategy