Efficient generation of adaptive Cartesian mesh for computational fluid dynamics using GPU

Mesh generation has been frequently the most time consuming step in typical CFD analysis studies. In the past two decades, adaptive Cartesian mesh methods have gained increasing popularity among CFD researches, mainly because of its simplicity and the possibility of automating mesh generation step. In contrast to body-fitted mesh, cells in Cartesian mesh are aligned with coordinate axes. In adaptive Cartesian mesh, cells near the objects' boundary are recursively refined using quad-tree (two-dimensional) or octree (three-dimensional). Then, cells intersecting the objects' boundary are clipped by the surfaces, leaving numerous small irregular shaped cells, called cut-cells. Most of the computational efforts required to generate adaptive Cartesian mesh is concentrated on the cut-cell clipping operation. To achieve the computational accuracy in the subsequent numerical solver, the number of cut-cells can be easily over millions, demanding substantial amount of computation time. Reducing mesh generation time matters more especially for unsteady flow simulation involving moving objects, which requires frequent regeneration of meshes for varied postures of the object. In this paper, we report an efficient novel approach to generating adaptive Cartesian mesh by parallelization using the graphics processing unit. The proposed method consists of the following three steps: (1) computing cross-sectional curves of object boundary, (2) octree refinement based on the section curves, and (3) cut-cell clipping. Because each step is designed to be highly parallelizable, we also implemented it on a graphics processing unit, showing orders of magnitude faster performance than the CPU version.