The Design of the Entropy Dissipator of the Entropy Dissipating Scheme for Scalar Conservation Law
The Design of the Entropy Dissipator of the Entropy Dissipating Scheme for Scalar Conservation Law
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发表时间：
2004
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通讯作者：
D. Mao
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作者：
D. Mao
在我们前面的论文[8]中，我们设计了一种具有分段线性重构的二阶Godunov型非线性保守差分格式，其中每个网格单元中重构函数的斜率可以通过耗散熵来计算。该方案满足熵条件，不仅计算数值解，而且计算数值熵；因此，它不同于以前所有的保守方案。该方案中的熵耗散器在计算过程中消散了每个网格单元中的熵，对稳定计算起到了重要作用。设计的熵耗散器相当复杂。在本文中，我们从数值上讨论了为什么必须消散熵以及应该消散多少熵。给出了一种新的基于数值解二阶差分的熵耗散器。数值例子展示了熵耗散器如何抑制不连续点附近的非物理振荡。
In our foregoing paper [8] we had designed a nonlinear conservative difference scheme of second-order Godunov type with piecewise-linear reconstruction,in which the slope of the reconstructed function in each grid cell can be computed by dissipating the entropy. Such a scheme satisfies the entropy condition,and computes not only numerical solution but also numerical entropy; thus, it is different from all former conservative schemes. A socalled entropy dissipator in the scheme, which dissipates the entropy in each grid cell in the computation, plays an important role in stabilizing the computation. The entropy dissipator designed in is quite complicated. In this paper, we numerically discuss why entropy must be dissipated and how much entropy should be dissipated. A new entropy dissipator, based on the second-order difference of the numerical solution is given. Numerical examples are presented to show how the entropy dissipator suppresses nonphysical oscillations near discontinuities.