Preconditioning Method Based On Cartesian Grids And Its Applications

Preconditioning method based on Cartesian grids was studied for simulating viscous low speed flows. It was successfully developed a solver for incompressibleviscous flow in low Mach number, using Cartesian grid and preconditioning method. It could effectively solve the problems of slow convergence and low precision of the former solver.First, we have studied the numerical methods based on adaptive Cartesian grids, a hybrid Cartesian grids method was studied by combining the technique of the hole-map and the method of the “donor cell” based on the ADT technique. The structured grid was adopted near the object surface while Cartesian grid was used for far field. Viscous flow problem of multi-element airfoil could be solved effectively.Then, the feasibility of the compressible equations solver of finite volume method was proved by successfully simulating the transonic flows past NACA0012 and cylinder. it was studied the application of two different preconditioning methods(Weiss-Smith and Choi-Merkle) to compressible equations solver. The pretreatment correction on HLLC data scheme was included, as well as the study of pretreatment time marching method based on implicit LU-SGS.Finally,This method which combines Cartesian grids and preconditioning method successfully simulated the viscous flows in low Mach number past NACA0012, cylinder and NLR-7301 multi-element airfoil. The numerical results agree well with the literature or experimental data, the convergence and effectiveness of the preconditioning method in this paper was proved. At the same time, the convergence effect of the two kinds of preconditioning methods were compared, and the different Mach number's influence on the rate of convergence is analyzed.