Atif Mohammad, Kolluru Praveen Kumar, Ansumali Santosh
Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India.
SankhyaSutra Labs Limited, Bangalore 560045, India.
Phys Rev E. 2022 Nov;106(5-2):055307. doi: 10.1103/PhysRevE.106.055307.
We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In this paper we explain the construction of closed-form analytic solutions to this equation. We demonstrate that near equilibrium this analytic solution reduces to the standard lattice Boltzmann model. We consider a few test cases to show that the analytic solution does not exhibit any significant deviation from the iterative solution. We also extend the analytical solution for the Ellipsoidal Statistical (ES)-Bhatnagar-Gross-Krook model to remove the limitation on the Prandtl number for heat transfer problems. The simplicity of the analytic solution removes the computational overhead and algorithmic complexity associated with the entropic lattice Boltzmann models.
我们详细描述了本质上基于熵的格子玻尔兹曼模型。熵格子玻尔兹曼模型通过迭代求解非线性熵演化方程来保证无条件数值稳定性。在本文中，我们解释了该方程封闭形式解析解的构建。我们证明，在接近平衡时，此解析解简化为标准格子玻尔兹曼模型。我们考虑了几个测试案例，以表明解析解与迭代解相比没有任何显著偏差。我们还扩展了椭球统计（ES）- Bhatnagar-Gross-Krook模型的解析解，以消除传热问题中普朗特数的限制。解析解的简单性消除了与熵格子玻尔兹曼模型相关的计算开销和算法复杂性。
