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Volume 24, Issue 3
Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant

Zhengfu Xu & Chi-Wang Shu

J. Comp. Math., 24 (2006), pp. 239-251.

Published online: 2006-06

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  • Abstract

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution.  

  • Keywords

Anti-diffusive flux correction, Sharpening contact discontinuity, High order accuracy, Finite difference WENO scheme, Saint-Venant system of shallow water, Transport of pollutant.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-239, author = {Zhengfu Xu and Chi-Wang Shu}, title = {Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {3}, pages = {239--251}, abstract = {

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8749.html} }
TY - JOUR T1 - Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant AU - Zhengfu Xu & Chi-Wang Shu JO - Journal of Computational Mathematics VL - 3 SP - 239 EP - 251 PY - 2006 DA - 2006/06 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8749.html KW - Anti-diffusive flux correction, Sharpening contact discontinuity, High order accuracy, Finite difference WENO scheme, Saint-Venant system of shallow water, Transport of pollutant. AB -

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution.  

Zhengfu Xu and Chi-Wang Shu. (2006). Anti-Diffusive Finite Difference WENO Methods for Shallow Water with Transport of Pollutant. Journal of Computational Mathematics. 24 (3). 239-251. doi:
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