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

2013 ◽  
Vol 14 (3) ◽  
pp. 664-702 ◽  
Author(s):  
Arthur Bousquet ◽  
Madalina Petcu ◽  
Ming-Cheng Shiue ◽  
Roger Temam ◽  
Joseph Tribbia
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water System ◽  
Limited Area ◽  
Two Dimensional ◽  
One Dimensional ◽  
Shallow Water System ◽  
The Waves

AbstractA 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.

scholarly journals AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL

2009 ◽  
Vol 19 (03) ◽  
pp. 477-499 ◽  
Author(s):  
JEAN DE DIEU ZABSONRÉ ◽  
CARINE LUCAS ◽  
ENRIQUE FERNÁNDEZ-NIETO
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Numerical Experiments ◽  
Water System ◽  
Two Dimensional ◽  
Sedimentation Model ◽  
Shallow Water System ◽  
Periodic Domains ◽  
The Stability

In this paper we consider a two-dimensional viscous sedimentation model which is a viscous Shallow–Water system coupled with a diffusive equation that describes the evolution of the bottom. For this model, we prove the stability of weak solutions for periodic domains and give some numerical experiments. We also discuss around various discharge quantity choices.

scholarly journals Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes

2013 ◽  
Vol 80 ◽  
pp. 441-452 ◽  
Author(s):  
Marc de la Asunción ◽  
Manuel J. Castro ◽  
E.D. Fernández-Nieto ◽  
José M. Mantas ◽  
Sergio Ortega Acosta ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Two Dimensional ◽  
Shallow Water System ◽  
Structured Meshes ◽  
Gpu Implementation

scholarly journals Admissibility conditions for Riemann data in shallow water theory

2020 ◽  
Vol 75 (7) ◽  
pp. 637-648
Author(s):  
Martin O. Paulsen ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
System Modeling ◽  
Water System ◽  
Shallow Water Theory ◽  
Constant Depth ◽  
Shallow Water System ◽  
Reasonable Sense

AbstractConsideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution of the Riemann problem associated to this system may feature dry states for some configurations of the Riemann data. This article will discuss various scenarios in which the Riemann problem for the shallow water system arises in a physically reasonable sense. In particular, it will be shown that if certain physical assumptions on the disposition of the Riemann data are made, then dry states can be avoided in the solution of the Riemann problem.

scholarly journals THREE-LAYER APPROXIMATION OF TWO-LAYER SHALLOW WATER EQUATIONS

2013 ◽  
Vol 18 (5) ◽  
pp. 675-693 ◽  
Author(s):  
Alina Chertock ◽  
Alexander Kurganov ◽  
Alexander Kurganov ◽  
Zhuolin Qu ◽  
Tong Wu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Water System ◽  
Single Layer ◽  
Inviscid Fluid ◽  
Layer Model ◽  
Momentum Exchange ◽  
Small Depth ◽  
Shallow Water System

Two-layer shallow water equations describe flows that consist of two layers of inviscid fluid of different (constant) densities flowing over bottom topography. Unlike the single-layer shallow water system, the two-layer one is only conditionally hyperbolic: the system loses its hyperbolicity because of the momentum exchange terms between the layers and as a result its solutions may develop instabilities. We study a three-layer approximation of the two-layer shallow water equations by introducing an intermediate layer of a small depth. We examine the hyperbolicity range of the three-layer model and demonstrate that while it still may lose hyperbolicity, the three-layer approximation may improve stability properties of the two-layer shallow water system.

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