Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

C.M. Klaij, Jacobus J.W. van der Vegt, H. van der Ven

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    Abstract

    The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a non-linear system of algebraic equations, which we solve with a local pseudo-time stepping method. Explicit Runge-Kutta methods developed for the Euler equations are unsuitable for this purpose as a severe stability constraint linked to the viscous part of the equations must be satisfied in boundary layers. In this paper, we investigate two new alternatives: \begin{enumerate} \item an implicit-explicit Runge-Kutta method, where the viscous terms are treated implicitly and the inviscid terms explicitly, \item a combination of two explicit Runge-Kutta schemes, one designed for inviscid flows and the other for viscous flows. \end{enumerate} We analyze the stability of the explicit and implicit-explicit methods, discuss their (dis)advantages and compare their performance by computing the flow around the NACA0012 airfoil at low and moderate Reynolds numbers.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    ISBN (Print)0169-2690
    Publication statusPublished - 2005

    Publication series

    NameMemoranda
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1782
    ISSN (Print)0169-2690

    Keywords

    • MSC-76N15
    • MSC-76M10
    • MSC-65M60
    • MSC-65L06
    • EWI-3602
    • IR-65966
    • METIS-226339

    Cite this

    Klaij, C. M., van der Vegt, J. J. W., & van der Ven, H. (2005). Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. (Memoranda; No. 1782). Enschede: University of Twente, Department of Applied Mathematics.