期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 24, 期 3, 页码 955-978出版社
SIAM PUBLICATIONS
DOI: 10.1137/S106482750139738X
关键词
finite-volume methods; high-resolution methods; conservation laws; source terms; discontinuous flux functions
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(i-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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据