High-order accurate p-multigrid discontinuous Galerkin solution of the Euler equations

Discontinuous Galerkin (DG) methods have proven to be perfectly suited for the construction of very high-order accurate numerical schemes on arbitrary unstructured and possibly nonconforming grids for a wide variety of applications, but are rather demanding in terms of computational resources. In order to improve the computational ef?ciency of this class of methods a p-multigrid solution strategy has been developed, which is based on a semi-implicit Runge–Kutta smoother for high-order polynomial approximations and the implicit Backward Euler smoother for piecewise constant approximations. The effectiveness of the proposed approach is demonstrated by comparison with p-multigrid schemes employing purely explicit smoothing operators for several 2D inviscid test cases.