An improved multigrid method for Euler equations

Abstract

A new full approximation storage multigrid method has been developed for Euler equations. Instead of the usual approach of using frozen τ (the relative truncation error between fine and coarse grid levels), the relative truncation error is distributed over coarse grids based on the solution of a set of model equations at every time step. This allows for more number of sweeps at coarse grid level. As a result, the present multigrid method is able to accelerate the solution at much faster rate than the conventional multigrid method. A first order Steger and Warming flux vector splitting strategy has been used here for solving Euler equations as well as the model equations for τ. Results are presented to demonstrate the ability of the present multigrid method.