Adaptive Mesh Fluid Simulations on GPU

TL;DR

This paper presents a GPU-accelerated adaptive mesh fluid simulation framework that significantly speeds up high-resolution shock capturing schemes, demonstrating scalability across multiple GPUs and extending to magneto-hydrodynamics.

Contribution

The authors develop a CUDA-based adaptive mesh refinement implementation for fluid simulations, achieving high speedups and extending applicability to more complex systems like MHD.

Findings

Approximately 10x speedup on a single GPU compared to CPU

Effective scaling up to four GPUs with near-ideal speedup

Framework adaptable to various conservation laws and higher-order schemes

Abstract

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.