Gpu techniques speed up turbulent flow simulations with mixed precision
Mixed-precision GPU algorithms for efficient turbulent flow simulations with Raviart-Thomas finite elements
Mathematical Software
Summary
Simulating turbulent flows in fluids is very complex and needs powerful computing. The authors develop new algorithms that run on graphics cards (GPUs) to solve these fluid equations more efficiently. They use a smart mix of single and double precision math to speed up calculations without losing accuracy in flow patterns. This approach makes the simulation faster by up to 70%, helping run detailed fluid studies more easily.
What this means in practice
- •For computational fluid dynamics engineers: Accelerate high-fidelity GPU-based simulations of incompressible turbulent flows using mixed-precision calculations that maintain key turbulence characteristics.
- •For gpu software developers: Implement efficient matrix-free operators and mixed-precision solvers for complex PDEs to reduce computation time in scientific GPU applications.
Authors
Ivan Prusak, Enes Mustafa Soydan, Ivan Pribec, Martin Kronbichler
Abstract
We propose GPU algorithms for high-fidelity simulation of incompressible turbulent flows. Discretization in space is performed with H(div)-conforming high-order Raviart-Thomas finite elements for the velocity and an $L^2$-conforming discontinuous Galerkin approximation for the pressure. In time, a consistent splitting scheme based on higher-order BDF time stepping is used, with convection treated explicitly. In this scheme, a pressure Poisson equation and a symmetric reaction-diffusion-type equation for the velocity need to be solved in each time step. We develop a solution framework with fast matrix-free operator evaluation for all ingredients, combined with multigrid solvers for the Poisson problem, and propose a robust mixed-precision algorithmic framework. A key to mixed-precision efficiency is a least-squares projection to generate accurate initial guesses for the iterative linear solvers, enabling us to work with relative residual tolerances of $10^{-3}$. In this regime, running the solvers entirely in single precision leads to almost no change in overall iteration counts and maintains the crucial turbulence statistics, while showing up to $1.7\times$ speedup over pure double-precision simulations.