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Generalization of a Relaxation Scheme for Systems of Forced Nonlinear Hyperbolic Conservation Laws with Spatially Dependent Flux Functions
Author(s) -
Montgomery Patrick J.,
Moodie T. Bryant
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00228
Subject(s) - conservation law , mathematics , nonlinear system , hyperbolic partial differential equation , burgers' equation , mathematical analysis , inviscid flow , boundary value problem , relaxation (psychology) , partial differential equation , initial value problem , forcing (mathematics) , shallow water equations , law , classical mechanics , physics , psychology , social psychology , quantum mechanics , political science
A generalization of a finite difference method for calculating numerical solutions to systems of nonlinear hyperbolic conservation laws in one spatial variable is investigated. A previously developed numerical technique called the relaxation method is modified from its initial application to solve initial value problems for systems of nonlinear hyperbolic conservation laws. The relaxation method is generalized in three ways herein to include problems involving any combination of the following factors: systems of nonlinear hyperbolic conservation laws with spatially dependent flux functions, nonzero forcing terms, and correctly posed boundary values. An initial value problem for the forced inviscid Burgers' equation is used as an example to show excellent agreement between theoretical solutions and numerical calculations. An initial boundary value problem consisting of a system of four partial differential equations based on the two‐layer shallow‐water equations is solved numerically to display a more general applicability of the method than was previously known.