Commun. Comput. Phys., 14 (2013), pp. 664-702.


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

Arthur Bousquet 1, Madalina Petcu 2, Ming-Cheng Shiue 3, Roger Temam 1*, Joseph Tribbia 4

1 The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA.
2 Laboratoire de Mathematiques et Applications, UMR 6086, Universite de Poitiers, France; The Institute of Mathematics of the Romanian Academy, Bucharest, Romania.
3 The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA; Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
4 National Center for Atmospheric Research, Boulder, Colorado, USA.

Received 7 March 2012; Accepted (in revised version) 6 November 2012
Available online 6 February 2013
doi:10.4208/cicp.070312.061112a

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.

AMS subject classifications: 35L04, 35Q35, 65M08, 65M55

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Key words: Boundary conditions, finite volumes, shallow water.

*Corresponding author.
Email: arthbous@indiana.edu (A. Bousquet), madalina.petcu@math.univ-poitiers.fr (M. Petcu), mingcheng.shiue@gmail.com (M. Shiue), temam@indiana.edu (R. Temam), tribbia@ucar.edu (J. Tribbia)
 

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