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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 = {A. Bousquet and A. Huang}, 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 AU - A. Bousquet & A. Huang 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 and A. Huang. (2014). 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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