| Large-scale scientific and engineering computing has become an equally important method in scientific research compared to experiment and theoretical research.The computing capacity of single-core processors is difficult to enhance because of the constraint by the development of hardware.And currently it falls far from the computing requirement of large-scale scientific and engineering computing.High-performance computing has been the only efficient way to meet such requirement.High-performance computing not only needs to be supported by good parallel computer system,but also requires advanced algorithms to solve large-scale scientific and engineering problems.The simulations of fluid flows have always been one of the most important areas in large-scale scientific and engineering computing,and are also a highly challenging task.The traditional way of solving Navier-Stokes equation needs the solution for large-scale algebraic equations.Explicit schemes of Navier-Stokes equation present better parallelism,but worse numerical stability and slow convergence speed while implicit schemes provide better numerical stability,faster convergence speed,but poor parallel scalability.All these greatly restrict the ability of solving Navier-Stokes equations.Based on the Boltzmann equations of mesoscopic model,the Lattice Boltzmann Methods(LBM) has recently become a new method of flow simulations.The inherent limitation of LBM methods leads to huge difficult in solving the problem of high-speed compressible,which significantly restrict the scope of application,although the advantages of this method are developed to be simple,capable of dealing with complex boundary conditions,natural parallel,etc.By developing new theory of the LBM methods, this paper works on high-speed compressible flow with large amount of numerical experiments,proved the correctness of compressible LBM methods,and performed the high-speed compressible LBM parallel algorithm with theoretical analysis and numerical experiments.Besides LBM method,Gas-Kinetic scheme(GKS) is also realized to be a new way for simulating fluid flow which built upon the Boltzmann equation.The method borrows ideas from finite volume,uses Boltzmann-BGK equation method for macro-physical flux on the control volume interface and establishes the area of control volume subdivision calculation.High-speed compressible flows problems then can be solved numerically.This paper presents a way of using unstructured mesh in Gas-Kinetic method for solving high-speed compressible flow problems with complicated boundary conditions, performs numerical experiments of the parallel algorithm on the three dimensional problem, and analyzes the scalability of the parallel algorithm.Finally,this paper compared these two Boltzmann based methods and put forward an idea of Lattice Boltzmann Gas-Kinetic Methods(LBGKM) method which merges these two methods.The innovative results in five aspects are described below:1.By investigating new theory of LBM methods for high-speed compressible flows. Develop TVD scheme used for classical LBM methods to simulate the shock wave phenomena and implement the effective algorithm.2.Study the parallelization of compressible LBM method.Evaluated the performance of parallel algorithm and put forward the ways of improving the parallel performance.3.Verify the new LBM theory in this paper through a large number of numerical experiments; achieve the parallel algorithm of three-dimensional problem and obtain the results of three-dimensional flow simulations.4.Use unstructured meshes for Gas-Kinetic method to solve complicated geometrical flow problems.Study the Gas-Kinetic method of both structured and unstructured meshes and develop the parallel algorithm based on Gas-Kinetic.Implement algorithms and obtain numerical results of simple 3-D high-speed flow.5.Fulfill 3-D parallel source codes LBM3D and GAS3D for new LBM and GKS algorithms, respectively,and solve 3-D high-speed compressible fluid flows in parallel.
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