High-order nonreflecting boundary conditions for the dispersive shallow water equations

Authors:
Dan Givoli;Beny Neta
Affiliations:
Department of Mathematics, Naval Postgraduate School, 1141 Cunningham Road, Monterey, CA;Department of Mathematics, Naval Postgraduate School, 1141 Cunningham Road, Monterey, CA
Venue:
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
Year:
2003

Citing 9
Cited 5

Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation

Mathematics of Computation
Finite difference schemes and partial differential equations

Finite difference schemes and partial differential equations
Radiation boundary conditions for dispersive waves

SIAM Journal on Numerical Analysis
A perfectly matched layer for the absorption of electromagnetic waves

Journal of Computational Physics
Exact nonreflecting boundary conditions for the time dependent wave equation

SIAM Journal on Applied Mathematics
A formulation of asymptotic and exact boundary conditions using local operators

Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Numerical solution of problems on unbounded domains. a review

Applied Numerical Mathematics - Special issue on absorbing boundary conditions
High-order nonreflecting boundary conditions without high-order derivatives

Journal of Computational Physics
High-order non-reflecting boundary scheme for time-dependent waves

Journal of Computational Physics

Lagrangian finite element modelling of dam-fluid interaction: Accurate absorbing boundary conditions

Computers and Structures
An experimental adaptation of Higdon-type non-reflecting boundary conditions to linear first-order systems

Journal of Computational and Applied Mathematics
Conservative finite difference schemes for the generalized Zakharov-Kuznetsov equations

Journal of Computational and Applied Mathematics
Improving the performance of Higdon non-reflecting boundary conditions by using weighted differencing

Applied Numerical Mathematics
A high-order based boundary condition for dynamic analysis of infinite reservoirs

Computers and Structures

Quantified Score

Hi-index	0.00

Visualization

Abstract

Time-dependent dispersive shallow water waves in an unbounded domain are considered. The infinite domain is truncated via an artificial boundary B, and a high-order non-reflecting boundary condition (NRBC) is imposed on B. Then the problem is solved by a finite difference scheme in the finite domain bounded by B. The sequence of NRBCs proposed by Higdon is used. However, in contrast to the original low-order implementation of the Higdon conditions, a new scheme is devised which allows the easy use of a Higdon-type NRBC of any desired order. In addition, a procedure for the automatic choice of the parameters appearing in the NRBC is proposed. The performance of the scheme is demonstrated via a numerical example.