GPU-Native Adaptive Mesh Refinement with Application to Lattice Boltzmann Simulations

TL;DR

This paper introduces a GPU-native adaptive mesh refinement algorithm using a block-based octree approach, significantly improving efficiency for Lattice Boltzmann simulations by eliminating CPU-GPU data transfers.

Contribution

It presents the first GPU-native AMR algorithm with a block-based octree method, fully implemented in CUDA, and validated on multiple hardware platforms for fluid flow simulations.

Findings

Efficient GPU-only AMR reduces data transfer overhead.

Validated with benchmarks on consumer and datacenter GPUs.

Applicable to various solvers on cell-centered grids.

Abstract

Adaptive Mesh Refinement (AMR) enables efficient computation of flows by providing high resolution in critical regions while allowing for coarsening in areas where fine detail is unnecessary. While early AMR software packages relied solely on CPU parallelization, the widespread adoption of heterogeneous computing systems has led to GPU-accelerated implementations. In these hybrid approaches, simulation data typically resides on the GPU, and mesh management and adaptation occur exclusively on the CPU, necessitating frequent data transfers between them. A more efficient strategy is to adapt and maintain the entire mesh structure exclusively on the GPU, eliminating these transfers. Because of its inherent parallelism, the Lattice Boltzmann Method (LBM) has been widely implemented in hybrid AMR frameworks. This work presents a GPU-native algorithm for AMR using a block-based forest of octrees approach, implemented in both two and three dimensions as open-source C++/CUDA code. The implementation includes a Lattice Boltzmann solver for weakly compressible flow, though the underlying grid refinement procedure is compatible with any solver operating on cell-centered block-based grids. The lid-driven cavity and flow past a square cylinder benchmarks validate the algorithm's effectiveness across multiple velocity sets in both single- and double-precision. Tests conducted on consumer and datacenter-grade GPUs demonstrate its versatility across different hardware platforms. Link to repository: https://github.com/KhodrJ/AGAL