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High‐order boundary conditions for linearized shallow water equations with stratification, dispersion and advection
Author(s) -
van Joolen Vince J.,
Neta Beny,
Givoli Dan
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.754
Subject(s) - stratification (seeds) , advection , bounded function , mathematics , boundary value problem , mathematical analysis , boundary (topology) , finite difference method , domain (mathematical analysis) , physics , seed dormancy , botany , germination , dormancy , biology , thermodynamics
Abstract The two‐dimensional linearized shallow water equations are considered in unbounded domains with density stratification. Wave dispersion and advection effects are also taken into account. The infinite domain is truncated via a rectangular artificial boundary ℬ, and a high‐order open boundary condition (OBC) is imposed on ℬ. Then the problem is solved numerically in the finite domain bounded by ℬ. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBCs originally proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis is on the effect of stratification. Published in 2004 by John Wiley & Sons, Ltd.