Institute of Aerodynamics and Fluid Mechanics, Technical University of Munich, 85748 Garching, Germany.
School of Mechanical Engineering, Shanghai Jiao Tong University, 200240 Shanghai, China.
Phys Rev E. 2018 May;97(5-1):053308. doi: 10.1103/PhysRevE.97.053308.
It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.
人们已经认识到，基于标准晶格的格子玻尔兹曼（LB）模型中存在额外的速度三次项。在这项工作中，研究了多相流拟位势 LB 模型中这些三次项的消除，其中考虑了力项和密度梯度。通过在平衡分布函数和离散力项中保留高阶（≥3）厄米特项，并在 LB 方程中引入修正项，可以完全消除速度的额外三次项。通过这种技术，可以很好地保持拟位势 LB 模型的计算简单性。进行了包括静止和移动的平面和圆形界面问题在内的数值测试，以显示这些三次项对多相流模拟的影响。结果表明，消除额外的三次项有助于减少数值误差，特别是当速度较大时。数值结果还表明，这些三次项主要在界面区域起作用，并且对于多相流而言，与密度梯度相关的三次项比其他三次项更为重要。
