An explicit gas kinetic scheme algorithm on non-uniform Cartesian meshes for GPGPU architectures

Abstract

We present an efficient algorithm of a two-dimensional Gas Kinetic Scheme (GKS) suitable for General Purpose Graphics Processing Units (GPGPUs). The algorithm features conservative second order quadtree-type refinement for Cartesian meshes and nested time stepping. The implementation is validated for several incompressible and thermal compressible test cases in the low Mach (Ma) number regime. We find that heat transfer for high Rayleigh (Ra) number and turbulent convection can be simulated correctly. Finally, we demonstrate a simulation of a Rayleigh-Bénard setup with Ra=1013 that qualitatively resembles the conditions of fire on a room scale. The implementation delivers a performance of more than one billion cell updates per second.