Transparent boundary conditions for the shallow water equations with a mixed finite element formulation

Authors:
Astrid Holstad;Ivar Lie
Affiliations:
Norwegian Meteorological Institute, P.O. Box 43 -Blindern, N-0313 Oslo, Norway;Norwegian Meteorological Institute, P.O. Box 43 -Blindern, N-0313 Oslo, Norway
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 11
Cited 0

On convergence of block-centered finite differences for elliptic-problems

SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems

SIAM Journal on Scientific Computing
Recent developments in the numerical simulation of shallow water equations I: boundary conditions

Selected papers of the IMACS conference on Innovative methods in numerical analysis
Inexact and preconditioned Uzawa algorithms for saddle point problems

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
A Galerkin-characteristic algorithm for transport-diffusion equations

SIAM Journal on Numerical Analysis
Numerical solution of problems on unbounded domains. a review

Applied Numerical Mathematics - Special issue on absorbing boundary conditions
LAPACK Users' guide (third ed.)

LAPACK Users' guide (third ed.)
Computer Methods for Partial Differential Equations: Elliptical Equations and the Finite Element Method

Computer Methods for Partial Differential Equations: Elliptical Equations and the Finite Element Method
Well-posed transparent boundary conditions for the shallow water equations

Applied Numerical Mathematics
Control-Volume Mixed Finite Element Methods

Control-Volume Mixed Finite Element Methods

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the application of characteristic-based transparent boundary conditions to the shallow water equations. A numerical method based on semi-Lagrangian time discretization and space discretization by the mixed finite element method, is presented in detail. The transparent boundary conditions are imposed weakly, which is natural for the space discretization we use.The numerical method is implemented in an experimental code, and several of the implementation aspects are addressed. Numerical experiments are presented showing that the boundary conditions allow both the outgoing waves to radiate out and the incoming waves to enter the domain in a transparent manner. The numerical results are also confirming previous theoretical results.