标题： 格子玻尔兹曼边界条件用于流体流动、对流扩散和磁流体力学模拟 显示英文标题

标题： Lattice Boltzmann Boundary Conditions for Flow, Convection-Diffusion and MHD Simulations

摘要： 提出了一种通用的推导方法，用于处理格子玻尔兹曼模拟中出现的各种边界条件。 提出了成对矩守恒的方法来强制执行具有特定宏观量的边界条件，包括流体模拟中的速度和压力边界条件、对流扩散（CD）模拟中的指定浓度以及磁流体力学（MHD）模拟中的指定磁场分量。 此外，CD 和 MHD 模拟可能分别涉及表面反应的罗宾边界条件和具有有限电导率的薄壁的类似罗宾边界条件，两者都可以写成包含可变通量项的形式。在这种情况下，所提出的边界方案将通量项作为反弹分布函数的增量，并使用参考框架变换来获得移动边界的校正项。对于计算网格点之间的任意边界位置，使用空间插值和外推法。由于推导过程中采用了相同的方法，在耦合模拟中不同物理过程得出的边界条件可以兼容于任意边界到网格的距离（不限于流行的半网格边界布局）和任意移动速度（不限于切向或法向速度）。进行了半网格和全网格边界布局的模拟以进行演示和验证。在流体动力学和 MHD 流动中模拟了移动边界，而在 CD 模拟中带有表面反应时使用静态边界。研究的数值解和解析解非常吻合。 显示英文摘要

摘要： A general derivation is proposed for several boundary conditions arisen in the lattice Boltzmann simulations of various physical problems. Pair-wise moment-conservations are proposed to enforce the boundary conditions with given macroscopic quantities, including the velocity and pressure boundary conditions in flow simulations, a given concentration in convection-diffusion (CD) simulations, as well as specified magnetic field components in magnetohydrodynamical (MHD) simulations. Additionally, the CD and MHD simulations might involve the Robin boundary condition for surface reactions and a Robin-like boundary condition for thin walls with finite electrical conductivities, respectively, both of which can be written in a form with a variable flux term. In this case, the proposed boundary scheme takes the flux term as an increment to the bounced distribution function and a reference frame transformation is used to obtain a correction term for moving boundaries. Spatial interpolation and extrapolation are used for arbitrary boundary locations between computational grid points. Due to using the same approach in derivations, the derived boundary conditions for different physical processes in a coupled simulation are compatible for arbitrary boundary-to-grid distances (not limited to the popular half-grid boundary layout) and arbitrary moving speeds (not limited to the tangential or normal speed). Simulations using half-grid and full-grid boundary layouts are conducted for demonstrations and validations. Moving boundaries are simulated in hydrodynamic and MHD flows, while static boundaries are used in the CD simulations with surface reactions. The numerical and analytical solutions are in excellent agreement in the studied cases.