Study On Lattice Boltzmann Method For Simplified Fluid Fluid Coupling Problem

Lattice Boltzmann method(LBM)is one of the popular numerical methods in computational fluid dynamics.Based on the perspective of micro-dynamics,LBM describes the macro-physical flow with the change of particle distribution function in time and space.In addition,LBM has the advantages of clear physical image,simple algorithm,and parallel nature.Since actual flow scenarios often involve the mutual coupling of multi-region and multi-physical fluid equations,it is difficult to effectively solve them using traditional numerical methods,and LBM provides effective solutions for such complex problems.This paper studies the application of LBM in the simplified fluidfluid coupling problem,the main work includes:Using LBM to solve the Heat-Heat coupling problem,and the lattice Boltzmann model of D2Q9 is established.First,the boundary conditions is discussed.The nonequilibrium extrapolation format is used to deal with the uncoupled boundary,and the iterative method is used to deal with the coupled boundary.Secondly,through multi-scale expansion,the established model is restored to the macroscopic heat equation.Finally,the model is verified by numerical simulation,and the result shows that the numerical solution and the analytical solution under the model are in good agreement.Using LBM to solve the Navier Stokes-Navier Stokes coupling problem,and the lattice Boltzmann modelof D2Q9 is constructed.when dealing with the coupling boundary,iterative relations are given for the nonlinear and linear forms respectively.In order to verify the validity of the model,the established model is restored to the original macroscopic equation through the Chapman-Enskog expansion.Finally,the twodimensional coupled Taylor-Green eddy current and the coupled square cavity flow were numerically simulated using the established model.