Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant

Journal of Computational Mathematics

Volumn 24, Issue 3, 2006, Pages 1-17

  Xu, Zhengfu ^a   Shu, Chi Wang ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

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

Indexed keywords

EID: 33744949897     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. F. Bouchut, An antidiffusive entropy scheme for monotone scalar conservation law, Journal of Scientific Computing, 21 (2004), pp.1-30.
2. M.-O. Bristeau and B. Perthame, Transport of pollutant in shallow water using kinetic schemes, in CEMRACS 1999, ESAIM Proceedings 10, Soc. Math. Appl. Indust., Paris 1999, pp.9-21.
3. A. Chertock, A. Kurganov and G. Petrova, Finite-volume-particle methods for models for transport of pollutant in shallow water, Journal of Scientific Computing, to appear. Appeared on line (2006). DOI: 10.1007/s10915-005-9060-x.
4. B. Despr´es and F. Lagouti`ere, Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, Journal of Scientific Computing, 16 (2001), pp.479-524.
5. A. Harten, The artificial compression method for computation of shocks and contact discontinuities: III, Mathematics of Computation, 32 (1978), pp.363-389.
6. A. Harten, ENO schemes with subcell resolution. Journal of Computational Physics, 83 (1989), pp.148-184.
7. A. Harten, B. Engquist, S. Osher and S. Chakravathy, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, 71 (1987), pp.231-303.
8. J.M. Hervouet, TELEMAC modelling system: an overview, Hydrological Processes, 14 (2000), pp.2209-2210.
9. G. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, Journal of Computational Physics, 126 (1996), pp.202-228.
10. X. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, Journal of Computational Physics, 115 (1994), pp.200-212.
11. P.L. Roe, Some contribution to the modelling of discontinuous flows, Lectures in Applied Mathematics 22 (1985), pp.163-193.
12. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, 1998, pp.325-432.
13. C.-W. Shu, High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD, International Journal of Computational Fluid Dynamics, 17 (2003), pp.107-118.
14. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of Computational Physics, 77 (1988), pp.439-471.
15. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock capturing schemes II, Journal of Computational Physics, 83 (1989), pp.32-78.
16. A.J.C. De Saint-Venant, Th´eorie du mouvement non-permanent des eaux, ave application aux crues des rivi`ere at `a l’introduction des mar´ees dans leur lit. Comptes rendus des seances de l’Academie des Sciences, Paris, 73 (1871), pp.147-154.
17. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM Journal on Numerical Analysis, 21 (1984), pp.995-1011.
18. Z. Xu and C.-W. Shu, Anti-diffusive flux corrections for high order finite difference WENO schemes, Journal of Computational Physics, 205 (2005), pp.458-485.
19. H. Yang, An artificial compression method for ENO schemes: the slope modification method, Journal of Computational Physics, 89 (1990), pp.125-160.