A wave-propagation method for conservation laws with spatially varying flux functions,
by D. S. Bale, R. J. LeVeque, S. Mitran, and J. A. Rossmanith, SIAM J. Sci. Comput 24 (2002), 955-978.

Abstract. We study a general approach to solving conservation laws of the form q_t+f(q,x)_x=0, where the flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function f_i(q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences f_i(Q_i)-f-1(Q_i-1) into eigenvectors of an approximate Jacobian matrix. This method is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities. Balance laws $q_t+f(q,x)_x=\psi(q,x)$ are also considered, in which case the source term is used to modify the flux difference before performing the wave decomposition, and an additional term is derived that must also be included to obtain full accuracy. This method is particularly useful for quasi-steady problems close to steady state.

SISC webpage for this paper

pdf file (39738.pdf: 481221 bytes)

Note: SIAM allows authors to post published papers on their website.

bibtex entry:
@Article{db-rjl-sm-jr:vcflux,
author = "D. Bale and R. J. LeVeque and S. Mitran and J. A. Rossmanith",
title = "A wave-propagation method for conservation laws and
balance laws with spatially varying flux functions",
journal = "SIAM J. Sci. Comput.",
year = "2002",
volume = "24",
pages = "955--978",
DOI = "10.1137/S106482750139738X",
}