On Increasing the Stability of the Combined Scheme of the Discontinuous Galerkin Method

摘要

Abstract— A special modification of the combined scheme of the discontinuous Galerkin method, which increases the stability of this scheme when calculating discontinuous solutions with shock waves, is proposed. This modification is related to the addition of artificial viscosity of the fourth order of divergence to the basic scheme included in this combined scheme. The test calculations are presented that demonstrate the advantages of the new combined scheme in comparison with the standard monotonic versions of the discontinuous Galerkin method.