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

Klaij, C.M. and Raalte van, M.H. and Ven van der, H. and Vegt van der, J.J.W. (2007) h-Multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations. Journal of Computational Physics, 227 (2). pp. 1024-1045. ISSN 0021-9991

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Abstract:	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.
Item Type:	Article
Copyright:	© 2007 Elsevier
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/62138
Official URL:	http://dx.doi.org/10.1016/j.jcp.2007.08.034
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