Research And Application Of Lattice Boltzmann Method With Multilayer And Adaptive Mesh

With the rapid development of high-performance computing technology,numerical computation method has become an important research method in parallel with theoretical analysis and experimental research,and plays an increasingly important role.Computational fluid dynamics,based on the basic theory and governing equations of fluid mechanics,combined with various numerical methods,such as finite difference method,finite element method,finite volume method,spectral method,wavelet method,relying on modern computer,has become an important research direction to solve various scientific and engineering problems of fluid mechanics.Computational fluid dynamics(CFD)plays an important role in the field of science and engineering.Lattice Boltzmann method(LBM),which was proposed in the late 1980 s,is a numerical method based on mesoscopic scale and gas kinetic theory.It has many advantages,such as clear physical background,linearization of main equations,natural locality and parallelism.It is very suitable for using parallel computing technology to solve complex flow problems,and has achieved great success in the field of fluid computing.LBM has many advantages,but it also has some defects.The standard LBM's discrete velocity model determines that it can only use uniform Cartesian mesh.If we want to obtain the local fine flow field in the computational domain,we need to use a smaller lattice size for the whole field,which will lead to a sharp increase in the amount of computation and reduce the computational efficiency,thus limiting the practical application of LBM.Therefore,a special mesh construction scheme is needed to improve the adaptability of LBM to complex fluid problems.The main work and innovation of this paper are as follows.1.A parallel algorithm of multi-layer mesh lattice Boltzmann is developed,which generates multi-layer mesh of different sizes in different computing domains.By setting a single layer buffer at the interface,the information transfer algorithm between coarse and fine mesh is optimized,and the time interpolation in the LBM of multi-layer mesh is avoided.The algorithm is based on the cell-center scheme and quadtree data structure.The mesh hierarchy is clear,and the additional numerical error and memory consumption caused by multiple interpolation processes are reduced.The excellent locality and computational accuracy of LBM are maintained,and the program implementation is more convenient.2.On the basis of multi-layer mesh LBM,a parallel algorithm of adaptive mesh refinement for LBM is developed,which can dynamically adjust the mesh structure according to the actual changes of physical quantities.Compared with the traditional CFD method,LBM needs to maintain more mesh topology information in the process of adaptive refinement and coarsening,so this paper optimizes the algorithm in the process of mesh structure reconfiguration,which effectively alleviates the conflict between computational accuracy and computational resource consumption.3.Aiming at the two different parallel programming modes of thread level parallelism based on Open MP and process level parallelism based on MPI,by binding threads and processes with computing cores and CPUs,the parallel speedup and computing efficiency are greatly improved.Aiming at the common cross-node parallel mode on the high-performance homogeneous computing platform,this paper combines the advantages of the two parallel programming modes.On the popular cluster supercomputer,the mixed programming of Open MP and MPI is applied,which effectively reduces the number of processes opened in the computing,reduces the overhead of the operating system scheduling process,and reduces the communication time between process,the parallel speedup and parallel efficiency are significantly improved.4.Based on C++ language,several sets of LBM parallel programs with good generality,expansibility and portability are developed,and the multi-layer mesh algorithm of single buffer,adaptive mesh refinement algorithm and Open MP-MPI hybrid programming parallel algorithm are realized,which are applied to solve many practical fluid mechanics problems.Numerical experiments are carried out on flow around a square cavity driven by a top cover,point source diffusion,circular cylinder,tandem double circular cylinder and NACA0012 airfoil.The accuracy and effectiveness of the proposed algorithm and the developed program are verified by comparing and analyzing the numerical results.