Comments on “A Spectral Limited-Area Formulation with Time-Dependent Boundary Conditions Applied to the Shallow-Water Equations”

1995 ◽  
Vol 123 (10) ◽  
pp. 3122-3123 ◽  
Author(s):  
Gábor Radnóti
Keyword(s):  
Boundary Conditions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Time Dependent ◽  
Limited Area

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.

A Conservative Formulation and a Numerical Algorithm for the Double-Gyre Nonlinear Shallow-Water Model

2015 ◽  
Vol 8 (4) ◽  
pp. 634-650 ◽  
Author(s):  
Dongyang Kuang ◽  
Long Lee
Keyword(s):  
Boundary Conditions ◽  
Shallow Water ◽  
Numerical Algorithm ◽  
Shallow Water Equations ◽  
Ocean Basin ◽  
Height Anomaly ◽  
Fractional Step ◽  
Step Algorithm ◽  
Gyre Circulation ◽  
Double Gyre

AbstractWe present a conservative formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean basin. The novelty of the paper is that we reformulate the governing equations into a nonlinear hyperbolic conservation law plus source terms. A second-order fractional-step algorithm is used to solve the reformulated equations. In the first step of the fractional-step algorithm, we solve the homogeneous hyperbolic shallow-water equations by the wave-propagation finite volume method. The resulting intermediate solution is then used as the initial condition for the initial-boundary value problem in the second step. As a result, the proposed method is not sensitive to the choice of viscosity and gives high-resolution results for coarse grids, as long as the Rossby deformation radius is resolved. We discuss the boundary conditions in each step, when no-slip boundary conditions are imposed to the problem. We validate the algorithm by a periodic flow on an f-plane with exact solutions. The order-of-accuracy for the proposed algorithm is tested numerically. We illustrate a quasi-steady-state solution of the double-gyre model via the height anomaly and the contour of stream function for the formation of double-gyre circulation in a closed basin. Our calculations are highly consistent with the results reported in the literature. Finally, we present an application, in which the double-gyre model is coupled with the advection equation for modeling transport of a pollutant in a closed ocean basin.

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