The Research On Modified Lattice Boltzmann Method And Large-Scale Parallel Computing

The large-scale science and engineering computing has become an important technology tool of scientific discovery and engineering design. Numerical simulation of complex fluid has been one of the most important and challenging areas in the largescale science and engineering computing. Di?erent from the classical numerical methods of continuum mechanics, lattice Boltzmann method(LBM) is a numerical method on the basis of molecular dynamics, which can be considered as a special form of discrete Boltzmann equation. Due to the characteristics of the kinematic on the Boltzmann equation, it can obtain Navier-Stokes equations according to the classical Chapman-Enskog expansion. So LBM contains more physical meanings than the Navier-Stokes equations based on the continuum hypothesis. Meanwhile, LBM includes these advantages of the simple algorithm, direct computation of pressure, easy handling of complex boundary conditions and especially suitable for parallel computing.Based on the above advantages of LBM, the development history of LBM, the common collision model(single relaxation(SRT) and multiple relaxation(MRT)) were described in detail. The conditions meeted by equilibrium distribution functions and the range of the original equilibrium distribution function itself were analyzed. The new equilibrium distribution functions in di?erent discrete velocity models derived from the continuous Maxwell equilibrium distribution function were investigated. In order to accelerate compute and treat complexity, the domain decomposition method and multigrid were applied to the LBM and the corresponding large-scale parallel algorithm was given.Since the method combines LBM and turbulence model of large eddy simulation(LES) can e?ectively simulate flow problems of high Reynolds number, the parallelism of LBM+LES was analyzed on the supercomputers with hundreds of thousands cores. The massively parallel computing model!algorithms and the implementation of highly scalable MPI program were given. Meanwhile, for better applying LBM+LES to the distributed shared memory architecture of clusters, LBM+LES with highly scalable parallel based on hybrid MPI+Open MP programming model was constructed. The correctness of the proposed model, the feasibility and high scalability of parallel algorithms were verified by large number of numerical experiments.The following four innovative points are achieved in this dissertations:1. Lattice Boltzmann method was deeply studied and the rate scope in equilibrium distribution function of classical Dn Qm discrete velocity model was analyzed. In order to enhance the range of the fluid flow rate, a new equilibrium distribution function derived from successive Maxwell equilibrium distribution functions to the corresponding discrete velocity model by a distribution function was proposed.The equilibrium distribution functions of two-dimensional D2Q9 model and threedimensional D3Q19 model were given respectively, which can be applied to greaterfluid flow rate range than before. Numerical solutions of cavity flow, flow around cylinder and a rear step flow have verified the validity of the equilibrium distribution functions;2. Based on MPI and MPI + Open MP of LBM+LES, highly scalable parallel algorithms suitable for large-scale computing were proposed respectively. Combined with parallel mesh generation, MPI communication modes of 2D and 3D mesh division were given. Large-scale computing experiments on /Zi Qiang 40000 clusters of Shanghai University and the /Sunway Blue Light0 supercomputer of National Supercomputing Center in Jinan verify high scalability of LBM+LES parallel algorithm for large scale problems, good speedup and e?ciency when 130,000 compute cores were used;3. Starting from a specific flow problems and considering di?erent convergence rate of di?erent computing region, an improved LBM based on block iterative strategy was proposed. The parallelism of proposed improved algorithm was analyzed and the corresponding Open MP parallel algorithms and program implemented were given.Numerical experiments show that this method can e?ectively reduce the number of iterations, accelerate the convergence rate and can be applied to a class of high Reynolds flow problems;4. In order to e?ciently use LBM in some complex local flow areas, a multi-grid lattice Boltzmann method was presented. Open MP parallelism of the method was also analyzed. The presented method establishes bu?er mainly on the interface between coarse and fine grid, which can reduce computing time on the interpolation and simplify the coupling relationship between coarse and fine grid. Compared with the original multi-block grid method, programming of the current method can be more convenient, and numerical experiments have verified the correctness of the method.