Abstract:

Turkel preconditioning matrix and multi-grid technique are combined to develop an efficient method suitable for numerical computation of low-speed viscous flow. Rigidity of the system of compressible Navier-Stokes equations is improved using the Turkel preconditioning matrix, thus the compressible range of Mach of two-dimensional flow is extended for low-speed flows. By using the LU-SGS (lower-upper symmetric Gauss-Seidel) implicit method and introducing preconditioning methods together with a multigrid scheme, an RAE2822 airfoil is simulated at low Reynolds number and a small angle of attack. Numerical results show that the preconditioning methods and multi-grid technique can greatly improve convergence of viscous flows. Besides, the above method can extend the computational domain of Mach number of compressible Navier-Stokes equations to a low-speed incompressible area, which is effective in calculating low-speed viscous flows.

Key words: low speed flow; multi-grid; preconditioning method; implicit method