Lattice boltzmann method for simulating the displacement of deformable membrane in fluid
用格子Boltzmann方法模拟流场中

A lattice Boltzmann method is employed to simulate the interaction between the deformable membrane and surrounding fluids. The boundary condition and the force exerting on the membrane are handled based on the lattice Boltzmann method. Interaction between the membrane and surrounding fluids may cause the membrane to vibrate. The membrane is discretized into segments. Each segment is simplified to a mass particle and connected to its neighbors. The Newtonian dynamic simulation is applied to each segment. The dynamic equation of the deformable membrane can be simulated according to the force acting on it. The hy-drodynamic forces acting on the membrane are obtained by the computation of fluid flow stress at the moving boundary using the lattice Boltzmann momentum-exchange method. It can simulate the curved shape with second-order accuracy. The fluid flow and membrane deformable equations are coupled. The membrane as a moving boundary affects the fluid flow, and the deformation of the membrane is the result of the hydrody-namic force acting on it. In this paper, the configurations of membranes at corresponding time under different conditions are computed. In the numerical test, both ends of the membrane are fixed and its initial shape is set to be a straight line, its initial vibrant velocity normal to the membrane surface is given to be varied at different position. The flow is simulated by the lattice Boltzmann method with second-order accuracy, and the deformation of the membrane is computed using the Newtonian dynamic equation. The results show that the configuration of the membrane is closed to its initial straight line in a sufficient long time if the membrane is relatively soft or stiff, and the results agree well with the other published results.