Research On Lattice Boltzmann Method And Its Parallel Algorithms

The lattice Boltzmann method(LBM)presented 30 years ago has achieved rapid development in theory and application.It has been able to solve practical problems in some engineering applications and has become a hot topic in related fields.LBM is different from the numerical methods to solve macroscopic equations(such as Navier-Stokes).It is based on the theory of molecular dynamics,which is derived from the Boltzmann equation.It can be seen as a discrete method on the macro level and a con-tinuous method on the micro level.Many traditional methods are not suitable for porous media,magnetic fluid,crystal growth and magnetic fluid,but LBM can be employed to simulate these applications.One of the most important advantage of LBM is that LBM has a natural parallel characteristic and is suitable for large-scale parallel clustering.Al-though LBM has achieved fruitful results,there are still many problems needed to be solved.The main work of this paper are listed as follows:1.Parallel methods of LBM on homogeneous and heterogeneous environment.In this paper,the multi-relaxation-time lattice Boltzmann method with large eddy simula-tion is adopted to simulate fluid flow with high Reynolds number and its parallel method is analyzed in detail.LBM is based on cartesian grid,so the flow field can be decomposed along the directions of the axes.Then the flow field is divided into many subdomains corresponding to the MPI processes.Each MPI process deal with a subdomain.In the homogeneous environment,the domain decomposition method(1D,2D and 3D)and the data exchange strategy are presented in detail.The way to judge the lattice type for complex boundary is described.The parallel performance is tested on the cluster of Shanghai university "Ziqiang 4000" and Sunway Blue Light MPP supercomputer in National Supercomputing center in Jinan.Three kinds of decom-position domain method,the judgement of lattice type and parallel performance are compared in detail.In the homogeneous multi-GPUs environment,the SoA scheme is employed to store variables in the global memory which can provide coalesced memory access and make full use of GPU memory bandwidth.In order to improve the efficiency,the subdomain is divided into two parts:inner and boundary.When the inner part is computed in the SMs,the data of boundary part is transferred through the overlap-ping mode to hide the communication time.The performance analysis is executed on 12 NVIDIA Kepler K20M GPUs.2.Parallel method of finite difference LBM.LBM can be treated as a particular case of finite difference LBM.Because of the Eulerian nature of the propagation step,temporal and spatial discretizations are decoupled so that the different spatial res-olutions irrespective of the time step are possible.The same parallel strategy is used to parallel finite difference LBM and the parallel performance is examined on Sunway Blue Light MPP supercomputer.3.A parallel lattice boltzmann model for high-speed compressible flow.LBM has been widely used for incompressible flow,but the compressible flow for high-speed is still in research.Based on Kun Qu's multi-speed model,a double-distribution-function model is presented by introducing an extra potential energy distribution function to recover Euler equations.The discretized lattice Boltzmann equations and the potential energy equations are solved by the third order monotone upwind scheme for scalar conservation laws finite volume method.In order to validate our mdoel,the flows past a bump in a channel,flows around Rae2822 airfoil and supersonic flow around a cylinder are simulated.In order to reduce the computa-tional time,a parallel method including the domain decomposition method,data exchange strategy is devised and tested on Tianhe-? in National Supercomputing center in Guangzhou.4.Finite volume LBM on unstructured grid.Although LBM on uniform grid is simple and suitable for parallel computing,it is difficult to judge the lattice type in flows with complicated geometries.Then,it has to enhance the resolution to improve the judgement which will lead to large computational time and grid.So the finite volume LBM is proposed.In 2D,the finite volume method is adopted to discrete the discrete velocity Boltz-mann equation with centroid-dual control volumes.The convective fluxes are eval-uated by Roe's flux-difference splitting scheme and the solution at the faces of the control volume is obtained by piecewise linear reconstruction of the left and right states.The gradients of particle distribution functions are computed with Green-Gauss approach.The present finite volume LBM is validated by three bench-mark flows:backward-facing step flow,lid-driven flow,flow around a cylinder and flow past a train.In 3D,we present a cell-centered finite volume LBM.The Lax-Wendroff scheme is adopted to compute the convective fluxes.The numerical validation is tested by three dimensional lid-driven flow.