Meshless Geometric Multigrid Method for Complex Geometries with Improved Cell Coarsening Algorithm

Abstract

In this paper, we present an improved multicloud methodology to extend the multicloud convergence accelerator, which depends on meshless discretization on coarse level computation of the geometric multigrid method, to cell finite volume (CFV) on three-dimensional space. To achieve this, we first identify the primary challenge in the meshless coarsening application to CFV. Specifically, the challenge lies in the poorly coarsened grid, which results in a degradation of the convergence rate. The reason for this is that the coarsening stencils were coupled with the discretization stencil. To address the issue, we proposed a new coarsening strategy on CFV that adequately utilizes node information on the fine-level mesh. The proposed methodology shows superior coarsening rates compared to the basic meshless cell coarsening, regardless of the dimension and type of mesh elements, resulting in significant speedup in convergence. Various computational fluid dynamics (CFD) simulations with three-dimensional complex geometries are presented, and their results demonstrate approximately seven times faster convergence compared to the single-grid method. The overall results verify that the multicloud method with the proposed coarsening procedure provides a powerful tool for practical CFD simulations by reducing the computation time, and it enables researchers and engineers to simulate and optimize real-world systems more efficiently.