Volume 28, Issue 6
A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations

Changna Lu, Jianxian Qiu & Ruyun Wang

J. Comp. Math., 28 (2010), pp. 807-825.

Published online: 2010-12

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  • Abstract

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.

  • Keywords

Numerical flux WENO finite volume scheme Shallow water equations

  • AMS Subject Headings

65M60 65M99 35L65.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-807, author = {}, title = {A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {6}, pages = {807--825}, abstract = {

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1001-m3122}, url = {http://global-sci.org/intro/article_detail/jcm/8551.html} }
TY - JOUR T1 - A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations JO - Journal of Computational Mathematics VL - 6 SP - 807 EP - 825 PY - 2010 DA - 2010/12 SN - 28 DO - http://doi.org/10.4208/jcm.1001-m3122 UR - https://global-sci.org/intro/article_detail/jcm/8551.html KW - Numerical flux KW - WENO finite volume scheme KW - Shallow water equations KW - AB -

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.

Changna Lu, Jianxian Qiu & Ruyun Wang. (1970). A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations. Journal of Computational Mathematics. 28 (6). 807-825. doi:10.4208/jcm.1001-m3122
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