Exploiting Properties of Entropy Symmetrization Variables to Simplify the Software Implementation of the Discontinuous Galerkin Method for Conservation Laws

摘要

A mathematical construction is presented that simplifies the calculation of upwind numerical fluxes in the discontinuous Galerkin (DG) method when entropy symmetrization variables are used. The construction obviates the need for the explicit calculation of left eigenvectors of the flux Jacobian matrices that usually appear in the calculation of upwind fluxes. This construction has been implemented in a finite element software library for general systems of conservation laws. The library is used in the software development of a general space-time discontinuous Galerkin method for compressible flow. This implementation permits both the primal analysis of compressible fluid flow as well as dual analysis for use in a posteriori error analysis and adaptive error control. Primal and dual computations of compressible flow are presented to demonstrate actual applications of the library.