LBM-FEM Coupled Two-grid Method And Its Local Parallel Algorithm

Lattice Boltzmann method(LBM)is a mesoscopic method for fluid flow modeling.In this thesis,the coupling of FEM and LBM is chosen to study the incompressible steady-state Navier Stokes problem,and two algorithms are proposed: the two-grid method of LBM-FEM and the local parallel algorithm of FEM-LBM.LBM-FEM two-grid method algorithm mainly uses the characteristics of LBM in solving the steady incomressible flow problem according to steady flow not sensitive to initial value and the idea of finite element two-grid method.First,LBM is applied to calculate the steady-state solution on a large(coarser)lattice,and then the solution is interpolated into the corresponding finer mesh finite element space.Then,on the finer mesh,the steady-state N-S solution is obtained by using the one-step Newton iterative scheme of FEM.Based on this algorithm,the steady incompressible flow problems(Taylor green flow,square cavity flow,etc.)are numerically simulated,and compared with the classical finite element two-grid method algorithm,the effectiveness and feasibility of the algorithm are proved.The main idea of local parallel algorithm of FEM-LBM is to use FEM to construct LBM subregions In this way,LBM can be paralleled independently in each subregion.Firstly,the boundary macro quantity needed by LBM is calculated by FEM in the whole region,and the macro quantity is interpolated into the finer lattice where LBM is located.Then,the macro quantity is reconstructed into the distribution function needed by LBM by using the reconstruction operator.Then,the whole region is decomposed into several sub regions,and the steady-state N-S solution is obtained by using LBM in the sub regions.Finally,the steady-state incompressible flow problems(Taylor green flow,square cavity flow,etc.)are solved based on this algorithm Numerical simulation.