Abstract:
In this paper, a precondition method based on hybrid Cartesian grid is used to simulate the steady and unsteady flow problems at low Mach number. In this method, the body-fitted structured grid is used around the body surface, and the Cartesian grid is then used in the left region. To transfer information between the two grids, the technique of searching donor cell is adopted. In addition, by using the density based precondition method, a N-S equation solver, which can solve flow problems ranging from very low Mach number to general Mach number, is developed. In this solver, the implicit dual-time stepping LU-SGS scheme is used for temporal discretization, and the cell-centered finite volume method with second-order accuracy is used for spatial discretization. To simulate unsteady flow, the flow field parameters on new presented cells are determined by using inverse distance interpolation. The numerical simulations of steady flow over a NACA0012 airfoil as well as unsteady flow with dynamic stall are performed. The generated results show that the use of precondition method at low Mach number can both accelerate the convergence of numerical calculation and improve the accuracy of solution. The developed N-S equation solver based on hybrid Cartesian grid can effectively simulate unsteady incompressible flow problems including moving boundary. Therefore, it can be inferred that to combine the precondition method with the hybrid Cartesian grid is a new way to solve the moving boundary problems with low Mach number and general Mach number.