GPU-native Embedding of Complex Geometries in Adaptive Octree Grids Applied to the Lattice Boltzmann Method

Abstract

Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for incorporating stationary triangle-mesh geometries into block-structured forest-of-octrees grids, performing both solid voxelization and automated near-wall refinement entirely on the device. The method employs local ray casting accelerated by a hierarchy of spatial bins, leveraging efficient grid-block traversal to eliminate the need for index orderings and hash tables commonly used in CPU pipelines, and enabling coalesced memory access without CPU-GPU synchronization. A flattened lookup table of cut-link distances between fluid and solid cells is constructed to support accurate interpolated bounce-back boundary conditions for the lattice Boltzmann method (LBM). We implement this approach as an extension of the AGAL framework for GPU-based AMR and benchmark the geometry module using the Stanford Bunny (112K triangles) and XYZ RGB Dragon (7.2M triangles) models from the Stanford 3D Scanning Repository. The extended solver is validated for external flows past a circular/square cylinder (2D, $Re = 100$), and a sphere (3D, $\text{Re}\in\{10, 15, 20\}$). Results demonstrate that geometry handling and interpolation impose modest overhead while delivering accurate force predictions and stable near-wall resolution on adaptive Cartesian grids. The approach is general and applicable to other explicit solvers requiring GPU-resident geometry embedding.