Cartesian Mesh-based Incompressible Flow Simulation over Arbitrarily Complex Geometries using a Multigrid Method

Abstract

In this dissertation, two algorithms for efficient Cartesian mesh-based flow simulations over arbitrarily complex objects are presented. As a first category of this dissertation, a geometric multigrid (MG) algorithm using the Heaviside function restriction is presented. This algorithm is simple to implement, readily parallelizable, and can be applied to any irregular domain problem. The validity of the presented algorithm is demonstrated by solving an analytically defined Poisson problem on an irregular domain. Furthermore, the optimal performance of the MG method is also demonstrated herein. As a second category of this dissertation, a novel efficient and reliable determination procedure of the signed distance function (SDF) based on an adaptive mesh refinement (AMR) strategy is described. Our motivation is that the SDF near the solid boundary is accurately required in the fluid simulation, whereas the SDF of the rest region can be considered as arbitrarily large values if the sign is correct. We employ the AMR procedure in order to efficiently define interface cells containing the solid boundary. By focusing on interface cells in hierarchical grids, the number of operations for computing the SDF can be reduced significantly. The efficiency and accuracy of the proposed method is demonstrated by volume convergence tests. By combining above two algorithms with an existing solution algorithm for the fluid, an inhouse Cartesian mesh-based incompressible flow solver is developed. The hybrid MPI/OpenMP parallelization is applied to this solver, and parallel computation is conducted on the KISTI`s Nurion supercomputer. To demonstrate applicability of the current approach, various well-known benchmark problems in both 2D and 3D are simulated, and all results are validated with previous experimental and numerical data. Furthermore, as the most challenging test case, simulations for flow over an underwater walking robot, namely Crabster, are presented. Finally, golf ball wake simulations with and without back-spin are presented as a very large-scale problem, which consists of ten-billions order cells.