High Density Ratio Multi-component Lattice Boltzmann Flow Model for Fluid Dynamics and Cuda Parallel Computation

The lattice Boltzmann equation (LBE) method is a promising technique for simulating fluid flows and modeling complex physics in fluids, and can be modified for solving general nonlinear partial differential equations (NPDEs). The LBE method has recently attracted more and more attention since it may help us to better understand the mechanisms of the complicated physical phenomena and dynamic processes modeled by NPDEs. In this dissertation, firstly, we developed a second-order accurate mass conserving boundary condition (BC) for the LBE method. Through several cases, the results show that our mass conserving BC will not result in the constant mass leakage that occurs for the other BCs in some cases. Additionally, it increases the efficiency and stability of the method for cases that involve relatively large magnitudes of body force. Secondly, we developed a multi-component and multi-phase LBE method for high density ratios. Multi-component multi-phase (MCMP) flow is very common in engineering or industrial problems and in nature. Because the lattice Boltzmann equation (LBE) model is based on microscopic models and mesoscopic kinetic equations, it offers many advantages for the study of multi-component or multi-phase flow problems. While the original formulation of Shan and Chen's (SC) model can incorporate some multiple phase and component scenarios, the density ratio of the different components is greatly restricted (less than approximately 2.0). This obviously limits the applications of this MCMP LBE model. Hence, based on the original SC iv MCMP model and the improvements in the single-component multi-phase (SCMP) flow model reported by Yuan and Schaefer, we have developed a new model that can simulate a MCMP system with a high density ratio. Finally, we developed a parallel computation LBE method based on Compute Unified Device Architecture (CUDA). CUDA offers a great economic alternative way to increase the calculation speed of LBE method instead of using a supercomputer. We present how to apply CUDA to the LBE method, including boundary condition treatments, single phase flow, thermal problems, and multi-phase cases. Through the results of several numerical experiments, our model with the help of CUDA can offer an improvement of a 10-30 times faster speed than that of a traditional single thread CPU code. 4.1 (a) Density contour for a circular droplet, (b) Comparison of the densities of the two components along the center line (50  y , 100 0   x