| 一维单个守恒律的一类二阶、几乎熵耗散的格式 |
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| 引用本文： | 刘相年,茅德康.一维单个守恒律的一类二阶、几乎熵耗散的格式[J].应用数学与计算数学学报,2003,17(2):15-24. |
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| 作者姓名： | 刘相年 茅德康 |
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| 作者单位： | 上海大学理学院,上海,200436 |
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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．
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| 关 键 词： | 守恒律 非线性稳定 熵耗散 差分格式 数值流函数 |
| 修稿时间： | 2003年3月18日 |
A Second-order Essentially Entropy-Dissipating Scheme for Scalar Conservation Law in One Space Dimension |
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| Liu Xiangnian Mao Dekang
School of Sciences,Shanghai University,Shanghai.A Second-order Essentially Entropy-Dissipating Scheme for Scalar Conservation Law in One Space Dimension[J].Communication on Applied Mathematics and Computation,2003,17(2):15-24. |
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| Authors: | Liu Xiangnian Mao Dekang
School of Sciences Shanghai University Shanghai |
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| Institution: | Liu Xiangnian Mao Dekang
School of Sciences,Shanghai University,Shanghai,200436 |
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| Abstract: | 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. |
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| Keywords: | conservation law nonlinear stability entropy-dissipation |
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