High Resolution Schemes and the Entropy Condition
High Resolution Schemes and the Entropy Condition
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DOI：
10.1007/978-3-642-60543-7_7
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发表时间：
1984-10
影响因子：
2.9
通讯作者：
S. Osher;S. Chakravarthy
中科院分区：
文献类型：
--
作者：
S. Osher;S. Chakravarthy
本文给出了构造半离散、二阶精度、变差递减、五点带宽、标量守恒律近似的系统方法。这些计划也满足一个单一的离散熵不等式。因此，在凸通量的情况下，我们证明收敛到唯一的物理正确的解决方案。对于双曲守恒律系统，我们正式使用这种结构来扩展第一作者的一阶精确方案，并显示（在一些小的技术假设下），极限解满足熵不等式。结果有关离散冲击，最大值原理，和最大阶精度。数值应用也提出。
A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five-point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, we prove convergence to the unique physically correct solution. For hyperbolic systems of conservation laws, we formally use this construction to extend the first author’s first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.