标题： 逐链人工可压缩性方法 显示英文标题

标题： Link-wise Artificial Compressibility Method

摘要： 人工可压缩性方法（ACM）用于不可压缩纳维-斯托克斯方程，通过在规则的笛卡尔网格上的一组离散方向（链接）进行重新表述（称为LW-ACM），类似于格子玻尔兹曼方法（LBM）。主要优势是能够利用最初为LBM和经典计算流体力学开发的成熟技术，特别强调有限差分（至少在本文中），只需进行少量修改。例如，与背景笛卡尔网格不对齐的壁面边界可以通过追踪每个链接与壁面的交点来考虑（类似于LBM技术）。LW-ACM不需要超出流体动力学的高阶矩（通常称为鬼影矩）和没有动能展开。像有限差分方案一样，只需标准泰勒展开即可进行一致性分析。初步的优化实现努力表明，LW-ACM的计算速度与优化的（BGK-）LBM相当。此外，内存需求显著小于（BGK-）LBM。重要的是，通过高效实现，该算法可能是少数几个计算密集型而非内存密集型的算法之一。研究了二维和三维基准问题，并与文献中的最新方法进行了广泛的比较研究。数值证据表明，LW-ACM在简单性、稳定性和准确性方面是一个极好的替代方案。 显示英文摘要

摘要： The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.