基于2D网格的轴对称浸没边界法

Immersed boundary methods is a common numerical simulation method to deal with moving boundary problems in particle two-phase flows. When the dimensionless parameters of studied physical problems meet certain requirements, its corresponding flow structure becomes axisymmetric. Hence, an axisymmetric immersed boundary method based on a 2D mesh and cylindrical coordinates is proposed in the present paper. A finite volume method is used as the spatial discretization in the present algorithm. And the governing equation is closed by a sharp stepped interface, which is used to replace the real solid immersed boundary. In order to improve the efficiency of computation, an adaptive mesh refinement technology is used to improve the mesh resolution near the immersed boundary. The using of cylindrical coordinates will produce a redundant source item from the viscous term in the momentum equation. The additional source term will be handled by using an implicit scheme. Moreover, in the direct numerical simulation of a sphere approaching a wall with a constant velocity, the pressure of the fluid in the gap dramatically changes because of the small gap. So, in order to accurately analyze the flow field, the required grid resolution is very high in the gap. Multiple projection-step calculations are carried out in one time step for maintaining the stability of the simulation. In the movement of a sphere free impacting a wall, a lubrication force model will be introduced to simulate the movement of the sphere near the wall even with a low grid resolution. Finally, simulation results on the flow past a fixed sphere, the flow past a circular disk, the stokes flow by a sphere approaching a wall and the flow caused by the sphere-wall collision prove that the present axisymmetric IBM algorithm is applicable and accurate for dealing with stationary and moving boundary problems in an axisymmetric flow.