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Volume 4, Issue 2
Momentum Conservative Schemes for Shallow Water Flows

S. R. Pudjaprasetya & I. Magdalena

East Asian J. Appl. Math., 4 (2014), pp. 152-165.

Published online: 2018-02

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  • Abstract

We discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

  • AMS Subject Headings

65M08, 76M12, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-152, author = {S. R. Pudjaprasetya and I. Magdalena}, title = {Momentum Conservative Schemes for Shallow Water Flows}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {2}, pages = {152--165}, abstract = {

We discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290913.170314a}, url = {http://global-sci.org/intro/article_detail/eajam/10829.html} }
TY - JOUR T1 - Momentum Conservative Schemes for Shallow Water Flows AU - S. R. Pudjaprasetya & I. Magdalena JO - East Asian Journal on Applied Mathematics VL - 2 SP - 152 EP - 165 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.290913.170314a UR - https://global-sci.org/intro/article_detail/eajam/10829.html KW - Finite volume method, staggered grid, conservative scheme, shallow water equations. AB -

We discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

S. R. Pudjaprasetya and I. Magdalena. (2018). Momentum Conservative Schemes for Shallow Water Flows. East Asian Journal on Applied Mathematics. 4 (2). 152-165. doi:10.4208/eajam.290913.170314a
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