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 highorder 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 efficiency 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.