Optimal Runge–Kutta smoothers for the p-multigrid discontinuous Galerkin solution of the 1D Euler equations

摘要: This work presents a family of original Runge–Kutta methods specifically designed to be effective relaxation schemes in the numerical solution steady state purely advective problems with high-order accurate discontinuous Galerkin space discretization and p-multigrid algorithm. The design criterion for construction here developed is different form one traditionally used derive optimal smoothers h-multigrid algorithm, which are order provide uniform damping error modes high-frequency range only. method proposed instead variable amount over entire frequency spectrum. performance assessed quasi one-dimensional Euler equations two test cases increasing difficulty. Some preliminary results showing multidimensional applications also presented.