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An immersed interface method for the Vortex-In-Cell algorithm

机译：Vortex-In-Cell算法的沉浸式接口方法

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The paper presents a two-dimensional immersed interface technique for the Vortex-In-Cell (VIC) method for simulation of flows past bodies of complex geometry. The particle-mesh VIC algorithm is augmented by a local particle-particle correction term in a Particle-Particle Particle-Mesh (P~3M) context to resolve sub-grid scales incurred by the presence of the immersed interface. The particle-particle correction furthermore allows to disjoin mesh and particle resolution by explicitly resolving sub-grid scales on the particles. This P~3M algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and adds an exact particle-particle correction term. Free-space boundary conditions are satisfied through the use of modified Green's functions in the solution of the Poisson equation for the streamfunction. The concept is extended such as to provide exact velocity predictions on the mesh with free-space boundary conditions. The random walk technique is employed for the diffusion in order to relax the need for a remeshing of the computational elements close to solid boundaries. A novel partial remeshing technique is introduced which only performs remeshing of the vortex elements which are located sufficiently distant from the immersed interfaces, thus maintaining a sufficient spatial representation of the vorticity field. Convergence of the present P~3M algorithm is demonstrated for a circular patch of vorticity. The immersed interface technique is applied to the flow past a circular cylinder at a Reynolds number of 3000 and the convergence of the method is demonstrated by a systematic refinement of the spatial parameters. Finally, the flow past a cactus-like geometry is considered to demonstrate the efficient handling of complex bluff body geometries. The simulations offer an insight into physically interesting flow behavior involving a temporarily negative total drag force on the section.
机译：本文提出了一种二维沉浸式界面技术，用于Vortex-In-Cell（VIC）方法，用于模拟流经复杂几何体的流。粒子-网格VIC算法在“粒子-粒子”-“粒子-网格”（P〜3M）上下文中增加了局部粒子-粒子校正项，以解决因浸没界面的存在而引起的子网格规模。此外，通过显式解析粒子上的子网格比例，粒子-粒子校正还可以使网格和粒子分辨率分离。该P〜3M算法使用影响矩阵技术来消除各向异性子网格规模，并添加精确的粒子-粒子校正项。通过在泊松方程的流函数解中使用改进的格林函数，可以满足自由空间边界条件。扩展了该概念，以便在具有自由空间边界条件的网格上提供精确的速度预测。随机游走技术被用于扩散，以便放松对重新排列靠近实体边界的计算元素的需求。引入了一种新颖的部分重新网格化技术，该技术仅对距沉浸界面足够远的涡旋元素进行重新网格化，从而保持了涡度场的足够空间表示。证明了目前的P〜3M算法具有收敛性。将沉浸式界面技术应用于流经圆柱的雷诺数为3000的流，并通过系统地优化空间参数来证明该方法的收敛性。最后，认为流过类似仙人掌的几何形状可以证明对复杂的钝体几何形状的有效处理。这些模拟提供了对有趣的物理流动行为的洞察力，其中涉及到截面上的临时负总阻力。

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