Simulation Of Flows With Moving Boundary By Lattice Boltzmann Method

The present thesis covers two main parts: the treatment for flow with moving boundary in lattice Boltzmann method, and the simulation of flow with moving boundary by lattice Boltzmann method.1. Treatment for flows with moving boundary in lattice Boltzmann methodHistorically the lattice Boltzmann method is evolved from lattice gas automata (LGA). It was proposed to simulate fluid dynamics by McNamara and Zanetti in 1988. The single-particle distribution function f i, average of Boolean variables is used to evolution directly. Lattice Boltzmann equation was used as the substitute the LGA evolution equation:Ω_α( f ( x , t)) is the collision operator. This model is called Lattice Boltzmann model.In 1989, Higuere and Jinenez proposed the model of linear collision operator. The equilibrium distribution function was used in this model. In 1989, Higuera, Succi and Benzi Constructed the equilibrium distribution function and collision matrix which is independent of LGA.In the above equation, e_α(α=0,1,…8) is the particle velocity in the a direction, f_α(x,t) is the density distribution function along the a direction, f_α^(eq)(x,t) is its corresponding equilibrium state, x is the spatial position vector, and t is the time,τis the dimensionless relaxation time andδ_t is time step.The discretized velocities of D2Q9 model is:The equilibrium distribution function of D2Q9 model is: in the above equation,We define an array to judge whether the crunode is a solid node or a fluid node and which region it belongs.The parameter define the fraction in fluid region of a grid spacing intersected by boundary: q_α(x) changes with time to track the boundary position accurately.Bounce-back scheme is the simplest boundary treatment in lattice Boltzmann method. The particles bounce back in the opposite direction original direction directly, the speed remains to same value.(α|-) is the opposite direction toα. x_f is the fluid note near by the boundary .Half-step bounce back scheme can achieve second-order accuracy.Our treatment for curved boundary is a combination of the bounce-back scheme and interpolations. When q≤1/ 2: When q >1/ 2:For moving boundary, the forcing item due to the fluid-wall interaction is: In the above equation,Some nodes become fluid nodes from solid nodes because of the boundary movement, their distribution functions can be given by the quadratic Lagrange extrapolation formula: Extrapolation direction is the opposite direction of the boundary velocity.Using the momentum-exchange method, the force on the boundary can be computed with:2. Simulation of flows with moving boundary by lattice Boltzmann methodWe investigate three cases of flow with moving boundary in this paper: the cylinder moving in the channel, the lid-driven cavity flow and a cylinder stiring in a cavity. The results of the simulation including the streamlines, vorticity contours, velocity distribution, lift and drag coefficients, velocity vector field etc. agree with those of available literatures, and show that LB method for flow with moving boundary can achieve accurate results and obtain the reasonable flow in detail.