An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems

摘要

We present a high-order formulation for solving hyperbolic conservation laws rising the discontinuous Galerkin method (DGM). We introduce an orthogonal basis for the spatial discretization and use explicit Runge-Kutta time discretization. Some results of higher order adaptive refinement calculations are presented for inviscid Rayleigh-Taylor flow instability and shock reflection problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities. [References: 22]