On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection–diffusion equation

In this paper a dual-compact scheme, which accommodates a better dispersion relation for the convective terms shown in the transport equation, is proposed to enhance the convective stability of the convection–diffusion equation by virtue of the increased dispersive accuracy. The dispersion-relation-...

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Bibliographic Details
Published in:Journal of computational physics 2009-06, Vol.228 (10), p.3640-3655
Main Authors: Chiu, P.H., Sheu, Tony W.H.
Format: Article
Language:English
Subjects:
Computational techniques
Convection–diffusion equation
Dispersion-relation-preserving
Dispersive accuracy
Dual-compact scheme
Exact sciences and technology
Mathematical methods in physics
Physics
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Summary:In this paper a dual-compact scheme, which accommodates a better dispersion relation for the convective terms shown in the transport equation, is proposed to enhance the convective stability of the convection–diffusion equation by virtue of the increased dispersive accuracy. The dispersion-relation-preserving compact scheme has been rigorously developed within the three-stencil point framework through the dispersion and dissipation analyses. To verify the proposed method, several problems that are amenable to the exact and benchmark solutions will be investigated. The results with good rates of convergence are demonstrated for all the investigated problems.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.02.008