A comparison between high-order temporal integration methods applied to the Discontinuous Galerkin discretized Euler equations

In this work we present a high-order Discontinuous Galerkin (DG) space approximation coupled with two high-order temporal integration methods for the numerical solution of time-dependent compressible flows. The time integration methods analyzed are the explicit Strong-Stability-Preserving Runge-Kutta (SSPRK) and the Two Implicit Advanced Step-point (TIAS) schemes. Their accuracy and efficiency are evaluated by means of an inviscid test case for which an exact solution is available. The study is carried out for several time-steps using different polynomial order approximations and several levels of grid refinement. The effect of mesh irregularities on the accuracy is also investigated by considering randomly perturbed meshes. The analysis of the results has the twofold objective of (i) assessing the performances of the temporal schemes in the context of the high-order DG discretization and (ii) determining if high-order implicit schemes can displace widely used high-order explicit schemes. © 2013 The Authors.