Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions.
Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions.
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DOI：
10.1103/physreve.86.025701
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
Alexander N Gorban;D. Packwood
中科院分区：
文献类型：
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作者：
Alexander N Gorban;D. Packwood
我们研究了在晶格玻尔兹曼方法中修改碰撞以保持适当的熵平衡的可能性。我们证明了在遵循玻尔兹曼H型定理的晶格玻尔兹曼方法作用的分布空间中，存在着一个可能与熵平衡发生碰撞的平衡点附近，同时存在着一个不可能与熵平衡发生碰撞的非平衡分布区域。特别地，对于具有正平衡的严格凹均匀有界熵函数，我们证明了适当的熵平衡总是可能足够接近局部平衡，而不可能足够远离它，在那里必须出现额外的耗散。我们还提出了一些非经典熵，它们不具有这种关注。分布进入远离平衡区域的情况通常发生在低粘度和/或高马赫数流动和粗网格模拟中。
We study the possibility of modifying collisions in the lattice Boltzmann method to keep the proper entropy balance. We demonstrate that in the space of distributions operated on by lattice Boltzmann methods which respect a Boltzmann type H theorem, there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exists a region of nonequilibrium distributions where such collisions are impossible. In particular, for a strictly concave and uniformly bounded entropy function with positive equilibria, we show that proper entropy balance is always possible sufficiently close to the local equilibrium and it is impossible sufficiently far from it, where additional dissipation has to appear. We also present some nonclassical entropies that do not share this concern. The cases where the distribution enters the region far from equilibrium typically occur in flows with low viscosity and/or high Mach number flows and in simulations on coarse grids.