Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations.

摘要: Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due their high-order accuracy geometric flexibility. However, DG is not perfect there remain some issues. Concerning robustness, has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear nonlinear problems. This chapter takes constructive approach introduce incarnation spectral element method compressible Navier-Stokes three-dimensional curvilinear context. The groundwork numerical scheme comes from classic principles including polynomial approximations Gauss-type quadratures. We identify aliasing as one underlying cause robustness issues classical methods. Removing said errors requires particular differentiation matrix careful discretization advective flux terms governing equations.