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

C.M. Klaij, M.H. van Raalte, H. van der Ven, J.J.W. van der Vegt
2007 Journal of Computational Physics  
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. Twolevel Fourier analysis of this method for the scalar advection-diffusion
more » ... n 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 ten w.r.t. singlegrid iterations.
doi:10.1016/j.jcp.2007.08.034 fatcat:gg6dkywyjnhijn2g5kg2os7cd4