h-Multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

Being implicit in time, the space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations requires the solution of a non-linear system of algebraic equations at each time-step. The overall performance, therefore, highly depends on the efficiency of the solver. In this article, we solve the system of algebraic equations with a h-multigrid method using explicit Runge-Kutta relaxation. Two-level Fourier analysis of this method for the scalar advection-diffusion equation shows convergence factors between 0.5 and 0.75. This motivates its application to the 3D compressible Navier-Stokes equations where numerical experiments show that the computational effort is significantly reduced, up to a factor 10 w.r.t. single-grid iterations.

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