Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method

摘要

In this paper, we describe an efficient method for simulating the two-dimensional steady and unsteady incompressible flows. The method is a hybrid approach, which combines the conventional finite difference (FD) scheme and the mesh-free least square-based finite difference (MLSFD) method. In this method, the MLSFD method is adopted to deal with the complex geometry for its "truly" mesh-free property, and it is responsible for the spatial discretization in the region around the complex geometry which represents the stationary solid obstacle. Correspondingly, conventional FD scheme is applied in the rest of the flow domain to take advantage of its high computational efficiency. Numerical simulation is carried out for the steady flow with Reynolds numbers of 10,20 and 40, and unsteady flow with Reynolds numbers of 100 and 200. The obtained numerical results agree very well with computational and experimental data available in the literature. Compared with the fully MLSFD method, this new approach greatly improves the computational efficiency.