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 oil 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 efficiency of this class of methods a p-multigrid Solution strategy has been developed, which is based oil 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. Copyright (C) 2008 John Wiley & Sons, Ltd.