Lattice Boltzmann method for the compressible Euler equations.
Lattice Boltzmann method for the compressible Euler equations.
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DOI：
10.1103/physreve.69.056702
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发表时间：
2004-05
期刊：
影响因子：
--
通讯作者：
T. Kataoka;M. Tsutahara
中科院分区：
文献类型：
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作者：
T. Kataoka;M. Tsutahara
提出了可压缩欧拉方程的格子Boltzmann模型及其严格的理论背景。该模型完全克服了以往模型中比热容比不能任意选取的缺陷。在小Knudsen数的限制下，如果解的变化是适度的，则从解获得的宏观变量满足可压缩Euler方程。这是没有冲击波或接触不连续出现的情况。相反，当解在几个局部区域由于激波和接触不连续的出现而急剧变化时，相应的宏观变量满足弱形式的欧拉方程。它们的推导是通过正确地考虑解的变化尺度而严格进行的。这是第一项研究，奠定了理论基础的格子玻尔兹曼模型的冲击波和接触不连续性的流动模拟。文中还给出了数值例子和误差估计，与上述理论结果一致。
The lattice Boltzmann model for the compressible Euler equations is proposed together with its rigorous theoretical background. The proposed model has completely overcome the defects of the previous model that the specific-heat ratio cannot be chosen freely. The macroscopic variables obtained from the solution are shown to satisfy, in the limit of the small Knudsen number, the compressible Euler equations if the variation of the solution is moderate. This is the case where no shock waves or contact discontinuities appear. In contrast, when the solution makes steep variation at several localized regions due to the appearance of shock waves and contact discontinuities, the corresponding macroscopic variables satisfy the weak form of the Euler equations. Their derivation is carried out rigorously by taking into account the scale of variation of the solution correctly. This is the first study that has laid the theoretical foundation of the lattice Boltzmann model for the simulation of flows with shock waves and contact discontinuities. Numerical examples and the error estimates are also given, which are consistent with the above theoretical arguments.