Comparing Active Flux and Discontinuous Galerkin Methods for Compressible Flow

摘要

A brief description is given of the Active Flux method for solving hyperbolic conservation laws. This method places emphasis on making a correct distinction between advective and acoustic modes of behavior. It leads naturally to a third-order accurate method. Results from this method are compared with those from discontinuous Galerkin methods having third-order accuracy on various simple test problems. It is found that the Active Flux method gives comparable levels of accuracy at substantially reduced cost.