A geometric multigrid accelerated incompressible flow simulation over complex geometries

Abstract

Two algorithms for a fast Cartesian mesh-based flow simulation over complex geometries are presented. As a first category, a geometric multigrid (MG) method using direct restriction of the Heaviside function, which is 0 in the body and 1 in the fluid, is presented. This method is easy to implement, readily parallelizable, and can be applied to any irregular domain. The validity and optimal performance of the current MG method are demonstrated by solving an analytically defined Poisson problem on an irregular domain. Another part of this paper is to introduce a novel efficient method for computing the signed distance function (SDF), which is a typical level-set value to represent bodies on Cartesian meshes. In the Cartesian mesh-based simulation, only the SDF near the body interface is accurately required. Based on this fact, the number of operations for computing the SDF can be significantly reduced by focusing on interface cells. In this study, the adaptive mesh refinement (AMR) strategy is employed to effectively trace the interface cells. By using these two algorithms, an in-house Cartesian mesh-based incompressible flow solver is developed. To demonstrate the applicability of the current approaches, well-known benchmark problems in 2D and 3D are simulated. Finally, as the most challenging case, simulations for flow over an underwater robot, namely Crabster, are presented.