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Title: SYSTEMS OF CONSERVATION LAWS

Abstract

A wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws. Among these schemes we determine the best ones, i.e., these which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2 to 3 meshpoints. These schemes are tested for stability and are found to be stable under a mild strengthening of the CourantFriedrichs-Lewy criterion. Test calculations of onedimensional flows of compressible fluids with shocks, rarefaction waves and contact discontinuities show excellent agreement with exact solutions. In particular, when Lagrange coordinates are used, there is no smearing of interfaces. The additional terms introduced into the difference scheme for the purpose of keeping the shock transition narrow are similar to, although not identical with, the artificial viscosity terms, and the like of them introduced by Richtmyer and von Neumann and elaborated by other workers in this field. (auth)

Authors:
;
Publication Date:
Research Org.:
Los Alamos Scientific Lab., N. Mex.
OSTI Identifier:
4244712
Report Number(s):
LA-2285
NSA Number:
NSA-13-011960
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Technical Report
Resource Relation:
Other Information: Orig. Receipt Date: 31-DEC-59
Country of Publication:
United States
Language:
English
Subject:
PHYSICS AND MATHEMATICS; COMPRESSIBILITY; CONSERVATION LAWS; DIFFERENTIAL EQUATIONS; ERRORS; FLUID FLOW; FLUIDS; PRESSURE; SHOCK WAVES; STABILITY; TESTING; TRANSIENTS; VISCOSITY

Citation Formats

Lax, P., and Wendroff, B. SYSTEMS OF CONSERVATION LAWS. United States: N. p., 1958. Web. doi:10.2172/4244712.
Lax, P., & Wendroff, B. SYSTEMS OF CONSERVATION LAWS. United States. doi:10.2172/4244712.
Lax, P., and Wendroff, B. Sat . "SYSTEMS OF CONSERVATION LAWS". United States. doi:10.2172/4244712. https://www.osti.gov/servlets/purl/4244712.
@article{osti_4244712,
title = {SYSTEMS OF CONSERVATION LAWS},
author = {Lax, P. and Wendroff, B.},
abstractNote = {A wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws. Among these schemes we determine the best ones, i.e., these which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2 to 3 meshpoints. These schemes are tested for stability and are found to be stable under a mild strengthening of the CourantFriedrichs-Lewy criterion. Test calculations of onedimensional flows of compressible fluids with shocks, rarefaction waves and contact discontinuities show excellent agreement with exact solutions. In particular, when Lagrange coordinates are used, there is no smearing of interfaces. The additional terms introduced into the difference scheme for the purpose of keeping the shock transition narrow are similar to, although not identical with, the artificial viscosity terms, and the like of them introduced by Richtmyer and von Neumann and elaborated by other workers in this field. (auth)},
doi = {10.2172/4244712},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Nov 01 00:00:00 EST 1958},
month = {Sat Nov 01 00:00:00 EST 1958}
}

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