skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nonreflecting boundary conditions for nonlinear hyperbolic systems

Abstract

Consider a nonlinear hyperbolic system ..nu../sub t/+A (..nu..) ..nu../sub chi/=0 for chi>0 and t>0. Suppose that the boundary chi=0 has been introduced only in order to limit the size of a computational problem. Suppose also that on physical grounds we know that no waves cross the boundary from the region chi>0. We need a boundary condition at chi=0 which expresses this fact. If our problem has no strong outgoing shocks, we may use the condition that at chi=0 the solution upsilon lies in the manifold generated by the Riemann invariants of the outgoing characteristics. For the equations of gas dynamics with an outflow boundary at chi=0 this condition may be written c/sub upsilon/..gamma..arho/sub t/+cupsilon..gamma..rho/sub t/+arhoS/sub t/=0, where a is the sound speed.

Authors:
Publication Date:
Research Org.:
Lawrence Livermore Laboratory, University of California, Livermore, California 94550
OSTI Identifier:
6143545
Resource Type:
Journal Article
Journal Name:
J. Comput. Phys.; (United States)
Additional Journal Information:
Journal Volume: 30:2
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DIFFERENTIAL EQUATIONS; BOUNDARY CONDITIONS; COMPUTER CALCULATIONS; GAS FLOW; NONLINEAR PROBLEMS; SHOCK WAVES; EQUATIONS; FLUID FLOW; 990200* - Mathematics & Computers

Citation Formats

Hedstrom, G.W. Nonreflecting boundary conditions for nonlinear hyperbolic systems. United States: N. p., 1979. Web. doi:10.1016/0021-9991(79)90100-1.
Hedstrom, G.W. Nonreflecting boundary conditions for nonlinear hyperbolic systems. United States. doi:10.1016/0021-9991(79)90100-1.
Hedstrom, G.W. Thu . "Nonreflecting boundary conditions for nonlinear hyperbolic systems". United States. doi:10.1016/0021-9991(79)90100-1.
@article{osti_6143545,
title = {Nonreflecting boundary conditions for nonlinear hyperbolic systems},
author = {Hedstrom, G.W.},
abstractNote = {Consider a nonlinear hyperbolic system ..nu../sub t/+A (..nu..) ..nu../sub chi/=0 for chi>0 and t>0. Suppose that the boundary chi=0 has been introduced only in order to limit the size of a computational problem. Suppose also that on physical grounds we know that no waves cross the boundary from the region chi>0. We need a boundary condition at chi=0 which expresses this fact. If our problem has no strong outgoing shocks, we may use the condition that at chi=0 the solution upsilon lies in the manifold generated by the Riemann invariants of the outgoing characteristics. For the equations of gas dynamics with an outflow boundary at chi=0 this condition may be written c/sub upsilon/..gamma..arho/sub t/+cupsilon..gamma..rho/sub t/+arhoS/sub t/=0, where a is the sound speed.},
doi = {10.1016/0021-9991(79)90100-1},
journal = {J. Comput. Phys.; (United States)},
number = ,
volume = 30:2,
place = {United States},
year = {1979},
month = {2}
}