Abstract: An LU-SGS based Choi-Merkle matrix preconditioning method is implemented within the framework of dual-time stepping and geometric multigrid method.An efficient method for steady and unsteady flows past aircraft configurations with Mach numbers from incompressible to transonic regime is developed.LU-SGS time stepping method is modified according to the preconditioned system.An efficient and robust splitting method for Jacobian matrix is presented.In simulation of viscous flows past NACA0012 airfoil ONERA M6 wing and DLR F4 wing/body configuration,the method obtains nearly Mach number-independent convergence at low-Mach numbers and improves efficiency slightly for transonic flows.Compared with Runge-Kutta based preconditioning method,LU-SGS based preconditioning method is more efficient.In simulation of unsteady viscous flow past an oscillating NACA 0012 airfoil convergence of sub iteration of dual time stepping is improved slightly.

Key words: Navier-Stokes equations, preconditioning method, LU-SGS scheme, multigrid method, numerical simulation