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Volume 4, Issue 4
Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization

Changna Lu & Gang Li

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 505-524.

Published online: 2011-04

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  • Abstract

In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.

  • Keywords

Multilevel time discretization, weighted essentially non-oscillatory schemes, shallow water equations, Runge-Kutta method, high order accuracy.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-505, author = {}, title = {Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {4}, pages = {505--524}, abstract = {

In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1027}, url = {http://global-sci.org/intro/article_detail/nmtma/5981.html} }
TY - JOUR T1 - Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 505 EP - 524 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1027 UR - https://global-sci.org/intro/article_detail/nmtma/5981.html KW - Multilevel time discretization, weighted essentially non-oscillatory schemes, shallow water equations, Runge-Kutta method, high order accuracy. AB -

In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.

Changna Lu & Gang Li. (2020). Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization. Numerical Mathematics: Theory, Methods and Applications. 4 (4). 505-524. doi:10.4208/nmtma.2011.m1027
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