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Boundary Conditions for Limited Area Models Based on the Shallow Water Equations

Published online by Cambridge University Press:  03 June 2015

Arthur Bousquet,
Madalina Petcu,
Ming-Cheng Shiue,
Roger Temam and
Joseph Tribbia
Arthur Bousquet*
Affiliation:
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA
Madalina Petcu*
Affiliation:
Laboratoire de Mathematiques et Applications, UMR 6086, Universite de Poitiers, FranceThe Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Ming-Cheng Shiue*
Affiliation:
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USADepartment of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan
Roger Temam*
Affiliation:
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA
Joseph Tribbia*
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado, USA
*
Email:madalina.petcu@math.univ-poitiers.fr
Email:mingcheng.shiue@gmail.com
Corresponding author.Email:temam@indiana.edu
Email:arthbous@indiana.edu
Email:tribbia@ucar.edu
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Abstract

A new set of boundary conditions has been derived by rigorous methods for the shallow water equations in a limited domain. The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions. The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain. The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

Keywords

35L0435Q3565M0865M55Boundary conditionsfinite volumesshallow water

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 3 , September 2013, pp. 664 - 702
Copyright
Copyright © Global Science Press Limited 2013

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