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首页> 外文期刊>Journal of Computational Physics >Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes
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Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes

机译：晶格Boltzmann方案中的物理解决方案超出了杂散的接口和边界行为

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The scalar field and the non-equilibrium solutions of the linear advection-diffusion d2Q9 Lattice Boltzmann (LBM) two-relaxation-times (TRT) scheme are constructed analytically. The scheme copes with an infinite number of suitable, second-order accurate, equilibrium weights. Here, the simplest, translation-invariant geometry with an implicitly located, straight or diagonal, grid-aligned interface (boundary) is addressed. We show that these two interface (boundary) orientations are accommodated with the help of two distinctive, anisotropic, discrete-exponential algebraic solution components, referred to as the A-layer and the B-layer. Being unpredicted by the perturbative analysis, such as the ChapmanEnskog, asymptotic or truncation, their solution is derived symbolically from the TRT recurrence equations, subject to the local mass conservation solvability and effective closure conditions. When the interface (boundary) is "diagonal", the A-layer perturbs the simplest physical solutions, like the piece-wise linear, polynomial or exponential scalar field, rendering the macroscopic solution weight-dependent and delaying its convergence to the first order; the A-layer base depends upon the weights, free relaxation parameter A and physical numbers. In contrast, the B-layer, invisible to the scalar field, typically accommodates the non-equilibrium discrepancy between the normal and diagonal directions on the "straight" interface (boundary); the B-layer base is fixed by A alone. The A-layer and B-layer may coexist and degrade the physical solution gradient and its convergence. Only the D2Q5 model is free from all these effects in the straight and diagonal orientations, while the diagonally-rotated D2Q5 model is unsuitable because of the "checkerboard" effect. These spurious corrections are not the Knudsen layers, but they present the LBM response for any-order bulk mismatch with the implicit or explicit interface (boundary) treatment; the A-layer and B-layer bring them in evidence and provide excellent benchmarks for their attenuation through interface-conjugate or adaptive refinement techniques. Our approach extends to any lattice, linear collision, source term, heterogeneity and LBM problem class. (C) 2020 Elsevier Inc. All rights reserved.
机译：用解析方法构造了线性对流扩散d2Q9格子Boltzmann（LBM）双弛豫时间（TRT）格式的标量场和非平衡解。该方案可处理无限多个合适的、二阶精度的平衡权重。这里，我们讨论了最简单的平移不变几何体，它有一个隐式定位的、直线的或对角线的、网格对齐的界面（边界）。我们表明，这两个界面（边界）方向是通过两个独特的各向异性离散指数代数解组件（称为A层和B层）来调节的。由于受到微扰分析（如ChapmanEnskog、渐近或截断）的不可预测性，它们的解从TRT递推方程中象征性地导出，服从局部质量守恒可解性和有效闭合条件。当界面（边界）为“对角”时，A层扰动最简单的物理解，如分段线性、多项式或指数标量场，使宏观解与权重相关，并延迟其收敛到一阶；A层基底取决于重量、自由松弛参数A和物理数。相比之下，标量场看不见的B层通常适应“直”界面（边界）上法线方向和对角线方向之间的非平衡差异；B层底座由A单独固定。A层和B层可能共存并降低物理解梯度及其收敛性。只有D2Q5模型在直线和对角线方向上不受所有这些影响，而对角线旋转的D2Q5模型由于“棋盘”效应而不适用。这些伪校正不是Knudsen层，但它们通过隐式或显式界面（边界）处理呈现出任何阶体失配的LBM响应；A层和B层为它们提供了证据，并通过界面共轭或自适应细化技术为它们的衰减提供了极好的基准。我们的方法扩展到任何晶格、线性碰撞、源项、异质性和LBM问题类。（C） 2020爱思唯尔公司版权所有。

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