An adaptive method with mesh moving and mesh refinement for solving the Euler equations

Abstract

We discuss mesh moving, local mesh refinement, and static mesh regeneration that are used with MacCormack's finite difference scheme to solve the Euler equations in two space dimensions. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh movement function so as to follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where the error estimates are high until a prescribed error tolerance is satisfied. The error estimation is based upon estimates of the local discretization error obtained by Richardson's extrapolation. A static mesh regeneration procedure is used to create the initial base mesh and a new base mesh when the existing one becomes too distorted through mesh movement. MacCormack's scheme is given total variation diminishing (TVD) artificial viscosity in order to compute shocks and discontinuities. The time step is adjusted automatically to maintain stable computation. Results are presented for a computational example.