Ye Zhao, Zhe Fan, Wei Li, Arie Kaufman and Suzanne Yoakum-Stover

1. Melting of a chocolate vase due to LBM-based hot air flow Lattice-Based Flow Simulation on GPU Ye Zhao, Zhe Fan, Wei Li, Arie Kaufman and Suzanne Yoakum-Stover Center for Visual Computing and Department of Computer Science, Stony Brook University http://www.cs.sunysb.edu/~vislab/projects/amorphous • Overview • A relatively new approach in computational fluid dynamics : Lattice Boltzmann Method (LBM) • A standard diffusion-advection equation of temperature with a finite-difference discretization • Couple the flow dynamics with thermal effects • Implement LBM and diffusion-advection computation on GPU • Thermal Effects • Model temperature dispersion by diffusion-advection equation • Discretized by finite difference operators with the same symmetry as the LBM lattice • Coupled to the LBM through the energy moment of each cell • Body forces introduced as momentum Bubbles and feather in wind field A cell of the lattice fi : particle distribution ei : velocity vector Decomposition of 13×13 2D matrix into 4×4 sub-matrices LBM-based flow with objects inside • LBM • Model Boltzmann particle dynamics on a lattice: a regular grid whose unit cell includes a center cell and links to neighbors • Each cell : Packet distributions, hydrodynamic moments, and velocity vectors to neighbors • LBM updates packet distribution through: • Collision: redistribution of packets at each cell • Streaming: packets move to neighbors along links • Density, velocity and momentum computed from packet distributions • Lends itself to parallel computation, complex boundaries, and multi-resolution • GPU Acceleration • Exploit locality and linearity of LBM • Map LBM operators onto GPU : group packet distributions and other properties into volumes and then packed into 2D textures • Fragment program updates distributions of every cell from its neighbors’ data • Matrix vector multiplication : decompose matrices and vectors into 4×4 matrices and 4-component vectors, then use built-in matrix-vector operations • Explicit finite difference straightforwardly computed on GPU Result Running time per step (in msec). Lattice resolution 50×50×50 SRTLBM : single-relaxation-time LBM, cannot couple thermal effects MRTLBM: multiple-relaxation-time LBM, results shown with and without thermal effects Acknowledgement: NSF CCR-0306438