### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

ISBN (Print) | 0169-2690 |

Publication status | Published - 2005 |

### Publication series

Name | Memoranda |
---|---|

Publisher | Department 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

*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.

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*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.

Research output: Book/Report › Report › Professional

TY - BOOK

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

AU - Klaij, C.M.

AU - van der Vegt, Jacobus J.W.

AU - van der Ven, H.

N1 - Imported from MEMORANDA

PY - 2005

Y1 - 2005

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

T3 - Memoranda

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

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -