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

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Klaij, C.M. and van der Vegt, J.J.W. and van der Ven, H. (2005) Pseudo-time stepping methods for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. [Report]

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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.
Item Type:Report
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65966
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