An Implicit Scheme For Incompressible LBGK Model And Analysis On Complex Boundary Processing

In recent years, the lattice Boltzmann method (LBM) is a new numerical scheme based on kinetic theory to simulate fluid flows. Compared with traditional computational approaches, the method is simple, intrinsically parallel, and easy to incorporate complex boundary conditions. Although the lattice Boltzmann method has achieved much success in fluid dynamics recently, there are still some problems needed to be solved, such as numerical instability and viscosity , complex boundary conditions and so on.In this paper we proposed an implicit scheme (also called -method) for LBGK model simulating incompressible fluids. The new parameter makes the model more flexible. Boundary conditions are treated briefly and it keeps the numerical accuracy of the LBM. From the numerical results of simulating Poiseuille flow in 2D with different values of the parameters, it is found that not only the numerical results were in good agreement with the analytic solutions but also the numerical accuracy and stability of the implicit scheme can be improved if some adaptable parameters are chosen. Second, curved boundary treatments for lattice Boltzmann method have been studied. And we have analyzed and compared their numerical accuracies and stabilities. Through the numerical simulations of two-dimensional Poiseuille flow and driven cavity flow on an equilateral triangle, the numerical accuracy and stability of the schemes have been discussed which was the foundation for using these schemes correctly. Finally, we proposed an improved thermal coupled lattice BGK model with a robust boundary scheme for complex boundary. In simulating the natural convection flow in a triangular enclosure with this scheme, the Rayleigh number can reach 108. In order to improve the numerical accuracy and stability, we implement the parallel version using MPI on the Lenovo DeepComp 1800 with 24 computing nodes due to the intrinsic parallelism of the method.