论文标题
矩形晶格网格上的预处理晶格玻尔兹曼方法，用于加速不均匀流的计算
Preconditioned Central Moment Lattice Boltzmann Method on a Rectangular Lattice Grid for Accelerated Computations of Inhomogeneous Flows
论文作者
论文摘要
通过预处理晶格Boltzmann（LB）方案可以实现流动模拟到其稳态的收敛加速度，从而减轻了相关的数值刚度，该方案迄今已在方形晶格上构建。我们通过求解预处理的Navier-Stokes（PNS）方程来有效地计算矩形晶格网格的新中央力矩LB方法，以有效地计算不均匀和各向异性流。矩平均校正是通过Chapman-Enskog分析得出的，该分析消除了由于使用矩形晶格而引起的网格 - 触觉造成的截短误差以及非加利亚不变的立方体速度误差引起的，这是由于对标准D2Q9 lattice的同样效果而导致的，以使标准D2Q9 lattice均可恢复pns pns sque erseations。这种校正取决于速度梯度的对角线成分，这些渐变梯度是从二阶非平衡矩从局部获得的，并由相关的网格纵横比$ r $ $ r $和预处理参数$γ$进行参数，并且碰撞模型中的声音速度自然通过物理一致的策略适应$ R $。我们通过使用强大的非正交矩基础来开发我们的方法，而中心矩平衡基于匹配原理，从而使使用矩形网格的校正更简单表达式，用于使用矩形网格，并将粘度作为放松参数，$ r $和$γ$的函数，$ r $和$γ$的函数，$ r $ and $γ$及其实现允许基于现有的平方lb schem lb schem lb schem s lb schem。使用预处理的矩形中央力矩LB方法对不均匀和各向异性剪切驱动的有界流的数值模拟证明了各种特征参数集的稳态的步骤数量的准确性和显着降低。
Convergence acceleration of flow simulations to their steady states at lower Mach numbers can be achieved via preconditioning the lattice Boltzmann (LB) schemes that alleviate the associated numerical stiffness, which have so far been constructed on square lattices. We present a new central moment LB method on rectangular lattice grids for efficient computations of inhomogeneous and anisotropic flows by solving the preconditioned Navier-Stokes (PNS) equations. Moment equilibria corrections are derived via a Chapman-Enskog analysis for eliminating the truncation errors due to grid-anisotropy arising from the use of the rectangular lattice and the non-Galilean invariant cubic velocity errors resulting from an aliasing effect on the standard D2Q9 lattice for consistently recovering the PNS equations. Such corrections depend on the diagonal components of the velocity gradients, which are locally obtained from the second order non-equilibrium moments and parameterized by an associated grid aspect ratio $r$ and a preconditioning parameter $γ$, and the speed of sound in the collision model is naturally adapted to $r$ via a physically consistent strategy. We develop our approach by using a robust non-orthogonal moment basis and the central moment equilibria are based on a matching principle, leading to simpler expressions for the corrections for using the rectangular grids and for representing the viscosities as functions of the relaxation parameters, $r$ and $γ$, and its implementation is modular allowing a ready extension of the existing LB schemes based on the square lattice. Numerical simulations of inhomogeneous and anisotropic shear-driven bounded flows using the preconditioned rectangular central moment LB method demonstrate the accuracy and significant reductions in the numbers of steps to reach the steady states for various sets of characteristic parameters.
