Transient fixed point-based unstructured mesh adaptation

This paper deals with adaptive simulation of time-dependent problems. Mesh adaptation for unsteady configurations is especially important as the phenomenon evolves in the whole computational domain and, in order to capture such a phenomenon accurately on adapted meshes, one has to predict the evolution path. Here, we propose a new adaptive algorithm for time-dependent simulation; the idea is to solve a transient fixed problem by introducing a new loop in the adaptation scheme. The metric used for 3D simulations is constructed with an a posteriori error estimate based on a discrete approximation of the Hessian of the solution. For time-dependent simulation, a metric intersection in time is introduced to refine all the areas where the phenomena evolve.