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Steady-state Two-relaxation-time Lattice Boltzmann formulation for transport and flow, closed with the compact multi-reflection boundary and interface-conjugate schemes
Journal of Computational Science ( IF 3.1 ) Pub Date : 2020-09-05 , DOI: 10.1016/j.jocs.2020.101215
Irina Ginzburg

We introduce the steady-state two-relaxation-time (TRT) Lattice Boltzmann method. Owing to the symmetry argument, the bulk system and the closure equations are all expressed in terms of the equilibrium and non-equilibrium unknowns with the half discrete velocity set. The local mass-conservation solvability condition is adjusted to match the stationary, but also the quasi-stationary, solutions of the standard TRT solver. Additionally, the developed compact, boundary and interface-conjugate, multi-reflection (MR) concept preserves the efficient directional bulk structure and shares its parametrization properties. The method is exemplified in grid-inclined stratified slabs for two-phase Stokes flow and the linear advection-diffusion equation featuring the discontinuous coefficients and sources. The piece-wise parabolic benchmark solutions are matched exactly with the novel Dirichlet, pressure-stress, Neumann flux and Robin MR schemes. The popular, anti-bounce-back and shape-fitted Dirichlet continuity schemes are improved in the presence of both interface-parallel and perpendicular advection velocity fields. The steady-state method brings numerous advantages: it skips transient numerical instability, overpasses severe von Neumann parameter range limitations, tolerates high physical contrasts and arbitrary MR coefficients. The method is promising for faster computation of Stokes/Brinkman/Darcy linear flows in heterogeneous soil, but also heat and mass transfer problems governed by an accurate boundary and interface treatment.



中文翻译:

稳态两弛豫时间格子Boltzmann公式用于传输和流动,采用紧凑的多反射边界和界面共轭方案来封闭

我们介绍了稳态两弛豫时间(TRT)的格子Boltzmann方法。由于对称性的原因,整体系统和闭合方程均以半离散速度集的平衡和非平衡未知数表示。调整局部质量守恒可解性条件,以使其与标准TRT求解器的固定解以及准平稳解相匹配。此外,已开发的紧凑型,边界型和界面共轭多反射(MR)概念保留了有效的定向体结构并共享其参数化特性。该方法以两相斯托克斯流的网格倾斜分层平板和具有不连续系数和源的线性对流扩散方程为例。分段抛物线基准解决方案与新型Dirichlet,压力应力,诺伊曼通量和Robin MR方案完全匹配。在界面平行和垂直对流速度场均存在的情况下,流行的,防反跳和形状拟合的Dirichlet连续性方案得到了改善。稳态方法具有许多优点:跳过了瞬态数值不稳定,超越了严格的冯·诺依曼参数范围限制,可以承受较高的物理对比度和任意的MR系数。该方法有望更快地计算非均质土壤中的斯托克斯/布林克曼/达西线性流,而且还可以通过精确的边界和界面处理来控制传热和传质问题。在同时存在界面平行和垂直对流速度场的情况下,改进了防反跳和形状拟合的Dirichlet连续性方案。稳态方法具有许多优点:跳过了瞬态数值不稳定,超越了严格的冯·诺依曼参数范围限制,可以承受较高的物理对比度和任意的MR系数。该方法有望更快地计算非均质土壤中的斯托克斯/布林克曼/达西线性流,而且还可以通过精确的边界和界面处理来控制传热和传质问题。在界面平行和垂直对流速度场均存在的情况下,防反跳和拟合形状的Dirichlet连续性方案得到了改善。稳态方法具有许多优点:跳过了瞬态数值不稳定,超越了严格的冯·诺依曼参数范围限制,可以承受较高的物理对比度和任意的MR系数。该方法有望更快地计算非均质土壤中的斯托克斯/布林克曼/达西线性流,而且还可以通过精确的边界和界面处理来控制传热和传质问题。超越了严格的冯·诺依曼(von Neumann)参数范围限制,可以承受较高的物理对比度和任意的MR系数。该方法有望更快地计算非均质土壤中的斯托克斯/布林克曼/达西线性流,而且还可以通过精确的边界和界面处理来控制传热和传质问题。超越了严格的冯·诺依曼(von Neumann)参数范围限制,可以承受较高的物理对比度和任意的MR系数。该方法有望更快地计算非均质土壤中的斯托克斯/布林克曼/达西线性流,而且还可以通过精确的边界和界面处理来控制传热和传质问题。

更新日期:2020-09-07
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