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Volume 11, Issue 4
Finite Volume Approximation of  the Linearized Shallow Water Equations in Hyperbolic Mode

A. Bousquet & A. Huang

Int. J. Numer. Anal. Mod., 11 (2014), pp. 816-840.

Published online: 2014-11

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  • Abstract

In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow $\tilde{u}_0$, $\tilde{v}_0$, and $\tilde{\phi}_0$ (sub- or super-critical flow at each part of the boundary). The three cases that we consider are fully hyperbolic modes.

  • Keywords

shallow water equations, finite volume method, stability and convergence.

  • AMS Subject Headings

35Q35, 65N08, 65N12, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-816, author = {}, title = {Finite Volume Approximation of  the Linearized Shallow Water Equations in Hyperbolic Mode}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {816--840}, abstract = {

In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow $\tilde{u}_0$, $\tilde{v}_0$, and $\tilde{\phi}_0$ (sub- or super-critical flow at each part of the boundary). The three cases that we consider are fully hyperbolic modes.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/553.html} }
TY - JOUR T1 - Finite Volume Approximation of  the Linearized Shallow Water Equations in Hyperbolic Mode JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 816 EP - 840 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/553.html KW - shallow water equations, finite volume method, stability and convergence. AB -

In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow $\tilde{u}_0$, $\tilde{v}_0$, and $\tilde{\phi}_0$ (sub- or super-critical flow at each part of the boundary). The three cases that we consider are fully hyperbolic modes.

A. Bousquet & A. Huang. (1970). Finite Volume Approximation of  the Linearized Shallow Water Equations in Hyperbolic Mode. International Journal of Numerical Analysis and Modeling. 11 (4). 816-840. doi:
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