Multigrid and Runge-Kutta time stepping applied to the uniformly non-oscillatory scheme for conservation laws

J.W. van der Burg; J.G.M. Kuerten; P.J. Zandbergen

doi:10.1007/BF00044333

Multigrid and Runge-Kutta time stepping applied to the uniformly non-oscillatory scheme for conservation laws

J.W. van der Burg, J.G.M. Kuerten, P.J. Zandbergen

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Abstract

It is known that Harten's uniformly non-oscillatory scheme is a second-order accurate scheme for discretizing coservation laws. In this paper a multigrid technique and Runge-Kutta time stepping with frozen dissipation is applied to Harten's scheme in order to obtain the steady-state solution. It is shown that these techniques applied to Harten's scheme lead to a better convergence to the steady-state solution of a first-order conservation law than applied to Jameson's scheme.

Original language	English
Pages (from-to)	243-263
Number of pages	21
Journal	Journal of engineering mathematics
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/BF00044333
Publication status	Published - 1991

Keywords

Mathematical modeling
Industrial mathematics
Good convergence
Accurate scheme
Scheme lead

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abstract = "It is known that Harten's uniformly non-oscillatory scheme is a second-order accurate scheme for discretizing coservation laws. In this paper a multigrid technique and Runge-Kutta time stepping with frozen dissipation is applied to Harten's scheme in order to obtain the steady-state solution. It is shown that these techniques applied to Harten's scheme lead to a better convergence to the steady-state solution of a first-order conservation law than applied to Jameson's scheme.",

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AU - Zandbergen, P.J.

PY - 1991

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AB - It is known that Harten's uniformly non-oscillatory scheme is a second-order accurate scheme for discretizing coservation laws. In this paper a multigrid technique and Runge-Kutta time stepping with frozen dissipation is applied to Harten's scheme in order to obtain the steady-state solution. It is shown that these techniques applied to Harten's scheme lead to a better convergence to the steady-state solution of a first-order conservation law than applied to Jameson's scheme.

KW - Mathematical modeling

KW - Industrial mathematics

KW - Good convergence

KW - Accurate scheme

KW - Scheme lead

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