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一维单个守恒律的一类二阶、几乎熵耗散的格式

A Second-order Essentially Entropy-Dissipating Scheme for Scalar Conservation Law in One Space Dimension
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摘要 本文考虑一维单个守恒律方程,对其设计了一个基于熵耗散的非线性守恒型差分格式.本格式的数值流函数是Lax-Freidrichs格式和Lax-Wendroff格式数值流函数的凸组合,凸组合中的系数是由考虑耗散熵来决定的.这样在解的光滑区域内,格式几乎、甚至完全是Lax-Wendroff格式,而在解的间断处,格式几乎、甚至完全是Lax-Freidrichs格式.从而消除了间断附近的非物理振荡,实现了计算的非线性稳定性.理论分析表明本格式在解的非极值点处是二阶精度的,而在解的极值点处至少有一阶精度.数值试验表明格式是有效的. In this paper, we are concerned with scalar conservation law in one space dimension, we design a nonlinear conservative difference scheme based on entropy-dissipation. The scheme's numerical flux is a convex combination of the Lax-Fridrichs and Lax-Wendroff scheme's fluxes. The coefficient of the combination is computed by the consideration of entropy dissipation. In smooth regions,the scheme is nearly or allmost Lax-Wendroff, and near discontinuities, the scheme is nearly or allmost Lax-Freidrichs. Numerical examples are presented to show the efficiency of the scheme.
作者 刘相年 茅德康
机构地区 上海大学理学院
出处 《应用数学与计算数学学报》 2003年第2期15-24,共10页 Communication on Applied Mathematics and Computation
关键词 守恒律 非线性稳定 熵耗散 差分格式 数值流函数 conservation law, nonlinear stability, entropy-dissipation
分类号 O411 [理学—理论物理]
  • 相关文献

参考文献14

  • 1Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys., 1983,49:357-393.
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二级参考文献11

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应用数学与计算数学学报
2003年 第2期

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