Lattice Boltzmann Simulations Of Flow Field And Its GPU-CUDA Massive Parallel Computing

Lattice Boltzmann Method (LBM) has been proved to be an efficient numerical method for simulating many complex fluid flows, such as multiphase flows, porous media, turbulent flows, etc. In contrast to the conventional numerical solution of macroscopic equation, i.e., Euler equation and Navier-Stokes equation, the LBM abstracts the fluid as many mesoscopic particles which will collide and stream in the simple lattice system in term of the mesoscopic kinetic theory, and the macroscopic variables of fluid flow will be computed by the time-space evolution of the statistical function which represents the particle distribution. Thus, the main advantages of using LBM include easy implementation of boundary conditions, short codes, simple programming and natural parallelism.In this study, the Smagorinsky eddy viscosity model is extended to the LBM for solving the incompressible flow field with high Reynolds number. Due to low computing efficiency of LBM for three-dimensional (3-D) problems with high Reynolds number, and the natural parallelism of LBM, and the limitations of the parallel computing based on CPU, the parallel programming model of Computing Unified Device Architecture (CUDA) based on the Graphic Processor Unit (GPU) is adopted to accelerate the parallel computing of LBM, and then the cavity flows and wind driven currents were numerically computed by the established parallel model. The main work of this study are follows:First, we introduce the history development, basic theory and model, boundary condition, unit conversion and the numerical implementation process on the LBM. For the simulations of incompressible flow field with high Reynolds number, the Smagorinsky eddy viscosity model is extended to the two-dimensional with nine velocities (D2Q9) and three-dimensional with nineteen velocities (D3Q19) Multiple Relaxation Time (MRT) lattice Boltzmann model based on the previous work, and then the D2Q9and D3Q19MRT-SMAG model are provided.Second, due to low computing efficiency of LBM for3-D problems with high Reynolds number, and the natural parallelism of LBM,, and the limitations of the parallel computing based on CPU,, the extended MRT-SMAG model was concurrently accelerated by the CUDA parallel programming model on GPU. In this part, we introduce the GPU-CUDA massive parallel programming model firstly, and then the implementation details of LBM with GPU-CUDA. By the analysis on the performance of the GPU-based parallel program, it can be concluded that the computational efficiency of the code could be improved by reasonable distribution of the number of thread in thread block, reducing the if judgment statements in the kernel function, using the high speed shared memory on chip as much as possible. To validate the code, the numerical experiment of Re=100003-D one-sided lid driven cavity flow which has the ratio of length, width and height is1:3:1was performed, the speedup is up to145times than CPU-only codes. Since the use of the same double precision in the GPU and the CPU codes, there is no accuracy mismatch problem.Third, due to the existed problem on the cavity flows, the numerical simulations of high Reynolds number two-dimensional (2-D) and3-D one-sided lid driven cavity flow, and3-D four-sided lid driven flow are researched by the established GPU-CUDA D2Q9and D3Q19MRT-SMAG model for further validating the established parallel model, assessing the capability of these models simulations of turbulent flows, and analyzing the flow field features in the multi-sided lid driven cavity. For2-D cavity flow, the transition Reynolds number which stands for the changing from laminar flow to turbulent flow in the cavity is analyzed, and the effects of the lattice grid system, Smagorinsky constant, initial running and time-averaged period on the mean macroscopic variables for high Reynolds number2-D cavity flow are discussed. For3-D one-sided lid driven cavity flow, it is proved that the MRT-SMAG model has the ability to solve the initial stage of3-D flow field, and the frictional effects of side wall on the flow pattern in the cavity are analyzed, and the two order statistics for the turbulent intensity are also discussed. For3-D four-sided lid driven cavity flow, the effects of transverse aspect ratio on the flow field features are discussed, and the multiple steady solutions (flow bifurcation) are computed. Also, the effects of various transverse aspect ratio on the multiple steady solutions which are produced when the flow is unstable are reported. In additional, the computational efficiency of the GPU-based parallel program for these examples is investigated.Fourth, a preliminary study of wind driven current is considered by the GPU-based parallel model. The time-averaged horizontal velocity profiles at different location on the symmetry plane are analyzed, and the velocity distributions on the inner-law coordinates relative to the shearing surface and bottom are presented. Then, the time averaged streamline contours and velocity vector on the symmetry plane are given. Also, the numerical results are validated by the laboratory experimental data. It is shown that the MRT-SMAG model has the ability to simulate the3-D wind driven current, and its the computing efficiency could be greatly improved by the CUDA parallel programming model on GPU, about178times.