Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws

The paper describes the construction of entropy-stable discontinuous Galerkin difference (DGD) discretizations for hyperbolic conservation laws on unstructured grids. takes advantage existing theory (diagonal-norm) summation-by-parts (SBP) discretizations. In particular, shows how DGD — both linear and nonlinear can be constructed by defining SBP trial test functions in terms interpolated degrees freedom. case discretizations, entropy variables rather than conservative must to nodes. A fully-discrete scheme is obtained adopting a relaxation Runge–Kutta version midpoint method. addition, matrix operators first derivative are shown dense-norm operators. Numerical results presented verify entropy-stability discretization context Euler equations. Accuracy studies reveal that method efficient; indeed, like tensor-product schemes, exhibits superconvergent solution error periodic problems. An investigation spectra spectral radius relatively insensitive order. Finally, applied one-dimensional Riemann problem, global convergence L1 norm observed.