3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations

This paper deals with the adaptation of unstructured meshes in three dimensions for transient problems with an emphasis on CFD simulations. The classical mesh adaptation scheme appears inappropriate when dealing with such problems. Hence, another approach based on a new mesh adaptation algorithm and a metric intersection in time procedure, suitable for capturing and track such phenomena, is proposed. More precisely, the classical approach is generalized by inserting a new specific loop in the main adaptation loop in order to solve a transient fixed point problem for the mesh–solution couple. To perform the anisotropic metric intersection operation, we apply the simultaneous reduction of the corresponding quadratic form. Regarding the adaptation scheme, an anisotropic geometric error estimate based on a bound of the interpolation error is proposed. The resulting computational metric is then defined using the Hessian of the solution. The mesh adaptation stage (surface and volume) is based on the generation, by global remeshing, of a unit mesh with respect to the prescribed metric. A 2D model problem is used to illustrate the difficulties encountered. Then, 2D and 3D complexes and representative examples are presented to demonstrate the efficiency of this method.