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Open boundary conditions for hyperbolic equations
Author(s) -
Lick Wilbert,
Ziegler Kirk,
Lick James
Publication year - 1987
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690030203
Subject(s) - mathematics , mathematical analysis , boundary (topology) , wave equation , boundary value problem , nonlinear system , point (geometry) , wave propagation , geometry , physics , optics , quantum mechanics
A previously developed general procedure for deriving accurate difference equations to describe conditions at open boundaries for hyperbolic equations is extended and further illustrated by means of several examples of practical importance. Problems include those with both incoming and outgoing waves at the boundary, the use of locally cylindrical and spherical wave approximations at each point of the boundary, and nonlinear wave propagation. Reflected waves in all cases are minimal and less than 10 −2 of the incident wave.