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ANTI-DIFFUSIVE FINITE DIFFERENCE WENO METHODS FOR SHALLOW WATER WITH TRANSPORT OF POLLUTANT 被引量：2

ANTI-DIFFUSIVE FINITE DIFFERENCE WENO METHODS FOR SHALLOW WATER WITH TRANSPORT OF POLLUTANT
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摘要 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 SaintVenant 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 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 SaintVenant 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
作者 Zhengfu Xu Chi-Wang Shu
机构地区 Department of Mathematics Division of Applied Mathematics
出处 《Journal of Computational Mathematics》 SCIE CSCD 2006年第3期239-251,共13页 计算数学（英文）
关键词 Anti-diffusive flux correction Sharpening contact discontinuity High order accuracy Finite difference WENO scheme Saint-Venant system of shallow water Transport of pollutant. Anti-diffusive flux correction, Sharpening contact discontinuity, High order accuracy, Finite difference WENO scheme, Saint-Venant system of shallow water, Transport of pollutant.
分类号 O241.82 [理学—计算数学]
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参考文献19

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同被引文献156

  • 1Minion M L. Semi-implicit spectral deferred correction methods for ordinary differential equations [ J]. Communications in Mathematical Sciences, 2003, 1: 471- 500.
  • 2Xia Y, Xu Y, Shu C-W. Efficient time discretization for local discontinuous Galerkin methods [J]. Discrete and Continuous Dynamical Systems-Series B, 2007, 8: 677- 693.
  • 3Strang G. On the construction and comparison of difference schemes [J]. SIAM Journal on Numerical Analysis, 1968, 5: 506- 517.
  • 4Shu C-W, Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes,Ⅱ[ J]. Journal of Computational Physics, 1989, 83: 32- 78.
  • 5Jiang G-S, Shu C-W. Efficient implementation of weighted ENO schemes [J]. Journal of Computational Physics, 1996, 126: 202- 228.
  • 6Shu C-W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws[ M]//Cockbum B, Johnson C, Shu C-W, Tadmor E (Editor: A Quarteroni), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics, volume 1697, Springer, 1998: 325- 432.
  • 7Roe P. Approximate Riemann solvers, parameter vectors and difference schemes [ J ]. Journal of Computational Physics, 1978, 27 : 1 -31.
  • 8Qiu j-x, Shu C-W. On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes [ J]. Journal of Computational Physics, 2002, 183:187 -209.
  • 9Merryman B. Understanding the Shu-Osher conservative finite difference form [ J]. Journal of Scientific Computing, 2003, 19:309 - 322.
  • 10Sebastian K, Shu C-W. Multi domain WENO finite difference method with interpolation at subdomain interfaces [J]. Journal of Scientific Computing, 2003, 19 : 405- 438.

引证文献2

二级引证文献24

Journal of Computational Mathematics
2006年 第3期

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