本文研究熵格子Boltzmann方法(ELBM)对于高Reynolds数流动问题的适用性。ELBM由于其满足热力学第二定律,使得它比标准的格子Boltzmann方法(LBM)具有更高的数值稳定性。ELBM在计算过程中,通过调节松弛参数来确保系统符合熵日定律。在调节松弛参数时,必须求解一个非线性方程组,这使得计算量加大。本文基于Ehrenfest理论,根据简单的正性约束来保证日定律的成立。在数值实例部分,对顶盖驱动流进行了研究,给出了此方法与上述方法计算效率和正确性的一个比较,并且研究了全局熵的变化。
The focus of this paper is on the applicability of entropic lattice Boltzmann method (ELBM) for high Reynolds number fluid flows. ELBM satisfies the second principle of thermodynamics, so ELBM possesses a stronger numerical stability compared with standard lattice Boltzmann method (LBM). In the process of implementing ELBM, the relaxation parameter is modified such that the population distributions of fluid systems satisfy the entropic H-theorem. When the relaxation parameter is adjusted, a nonlinear equation must be solved. So, ELBM need much more computation costs than that of the standard LBM. Based on Ehrenfest's theory, a simple positivity-enforcing constraint is adopted to guarantee the H-theorem. Numerical simulation of the lid-driven fluid flows is conducted to show the feasibility and efficiency of the proposed method.