### 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 language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

ISBN (Print) | 0169-2690 |

Publication status | Published - 2005 |

### Publication series

Name | Memoranda |
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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

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.