A preconditioned dual time-stepping procedure coupled with matrix-free LU-SGS scheme for unsteady low speed viscous flows with moving objects

摘要

In this paper an effective method is developed to solve unsteady low speed viscous flow problems with moving objects by using the governing equations of compressible fluids. The method is based on a dual time-stepping scheme, combined with low Mach number preconditioning and an implicit matrix-free Lower-Upper Symmetric Gauss-Seidel iteration on unstructured dynamic meshes. Because preconditioning modifies the governing equations, that induces the change of system's eigenvalues and eigenvectors, characteristic boundary conditions are also modified to suit the preconditioned characteristic system. Several test cases are simulated, including an in-line oscillating cylinder in a fluid at rest, flow over a flapping NACA0014 airfoil and low speed flow past a flapping-wing micro-air vehicle. Compared with experimental results whenever possible, the computed results indicate that this algorithm shows satisfactory improvement of solution efficiency and accuracy for low speed flow problems.