MacCormack's method for advection-reaction equations

D.F. Griffiths; D.J. Higham

MacCormack's method for advection-reaction equations

D.F. Griffiths, D.J. Higham

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic problems. Here, we consider MacCormack's method applied to the linear advection equation with nonlinear source term. Various features of the method are analysed. First, we show that the conventional implementation is not stable for Courant numbers close to one unless a small time-step is used.

Original language	English
Journal	Computational Fluid Dynamics Journal
Volume	9
Issue number	1
Publication status	Published - 2000

Keywords

advection-reaction equations
mathematics
fluid dynamics

Cite this

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AB - MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic problems. Here, we consider MacCormack's method applied to the linear advection equation with nonlinear source term. Various features of the method are analysed. First, we show that the conventional implementation is not stable for Courant numbers close to one unless a small time-step is used.

KW - advection-reaction equations

KW - mathematics

KW - fluid dynamics

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JF - Computational Fluid Dynamics Journal

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MacCormack's method for advection-reaction equations

Abstract

Keywords

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