A p-multigrid flux reconstruction method for the steady Navier-Stokes equations at low Mach numbers

摘要

A p-multigrid solver is developed for the steady Navier-Stokes equations at low Mach numbers. The flux reconstruction method is used for spatial discretization. To alleviate the stiffness of the compressible Navier-Stokes equations when Ma number is small, the local preconditioning technique is utilized. To minimize the memory usage, the element-Jacobi smoother is employed at different p-levels in the p-multigrid solver. Our numerical experiments have demonstrated that the p-multigrid solver can significantly increase the convergence speed when compared to a single-level smoothing method. For a p-multigrid solver, a {P_0 - P_0/2 - P_0/4} hierarchy of polynomial degrees is suggested to achieve optimal convergence speed. The p-multigrid solver has also been applied to simulate a steady flow over the SD7003 airfoil with highly anisotropic elements near boundaries.