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

Research output: Book/ReportReportProfessional

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

Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. / Klaij, C.M.; van der Vegt, Jacobus J.W.; van der Ven, H.

Enschede : University of Twente, Department of Applied Mathematics, 2005. (Memoranda; No. 1782).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations

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AU - van der Ven, H.

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PY - 2005

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N2 - 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.

AB - 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.

KW - MSC-76N15

KW - MSC-76M10

KW - MSC-65M60

KW - MSC-65L06

KW - EWI-3602

KW - IR-65966

KW - METIS-226339

M3 - Report

SN - 0169-2690

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

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Klaij CM, van der Vegt JJW, van der Ven H. Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Enschede: University of Twente, Department of Applied Mathematics, 2005. (Memoranda; 1782).