Towards a GPU-Native Adaptive Mesh Refinement Scheme for the Lattice Boltzmann Method in Complex Geometries

TL;DR

This paper introduces a GPU-native adaptive mesh refinement scheme for the Lattice Boltzmann Method that handles complex geometries directly on the GPU, enabling efficient flow simulations over irregular surfaces.

Contribution

The work presents a novel GPU-based AMR procedure integrated with complex geometry handling for LBM, allowing entirely GPU-resident mesh adaptation and boundary detection.

Findings

Achieved significant speedup over CPU implementation.

Successfully handled complex geometries like Stanford bunny.

Validated the method with 2D and 3D test cases.

Abstract

We present a GPU-native mesh adaptation procedure that incorporates a complex geometry represented with a triangle mesh within a primary Cartesian computational grid organized as a forest of octrees. A C++/CUDA program implements the procedure for execution on a single GPU as part of a new module with the AGAL framework, which was originally developed for GPU-native adaptive mesh refinement (AMR) and fluid flow simulation with the Lattice Boltzmann Method (LBM). Traditional LBM is limited to grids with regular prismatic cells with domain boundaries aligned with the cell faces. This work is a first step towards an implementation of the LBM that can simulate flow over irregular surfaces while retaining both adaptation of the mesh and the temporal integration routines entirely on the GPU. Geometries can be inputted as a text file (which generates primitive objects such as circles and spheres) or as an STL file (which can be generated by most 3D modeling software). The procedure is divided into three steps: 1) an import step where the geometry is loaded into either an index list arrangement or directly as a face-vertex coordinates list, 2) a spatial binning step where the faces are distributed to a set of bins with user-defined density, and 3) a near-wall refinement step where the cells of the computational grid detect adjacency to the faces stored in the appropriate bin to form the links between the geometry and the boundary nodes. We validate the implementation and assess its performance in terms of total execution time and speedup relative to a serial CPU implementation using a 2D circle and a 3D Stanford bunny.