Effect of Polynomial Degree on Discontinuous Galerkin Simulation of Euler Equations

Second order finite volume algorithms have long been used for robust simulation of compressible flows. Discontinuous Galerkin methods constitute one part of a suite of algorithms being developed for high order accurate simulations of such flows. These methods rely on a concept called limiter for stable computation of discontinuous flows. In general, these limiters introduce additional dissipation near discontinuities by locally compromising on the high order accuracy to some extent. For assessing the benefit of a high order simulation employing such a limiter, a shock tube problem and two shock interaction problems are simulated at different resolutions, using several polynomial degrees. Results obtained in these cases show that in flows with smooth variation and/or weak discontinuities, higher order simulations give more accurate results, and this improvement is more marked at lower resolutions. In flows having strong discontinuities, the performance improvement in using higher than quadratic basis is minimal. The relative cost is similar for simulations using quadratic and higher basis.