Low Mach Number Local Preconditioning for Unsteady Viscous Finite Volumes Simulations on 3D Unstructured Grids

This paper presents a density-based finite volumes method for solving the unsteady Navier-Stokes equations on 3D unstructured grids. The second order Crank-Nicolson scheme is applied to perform the time integration. At each time step, the system of non linear equations is solved by means of a fully implicit dual time stepping method. An eigenvalues analysis demonstrates that this system can be ill-conditioned in the case of low Mach number flows for a certain range of CFL numbers. A new unsteady preconditioning technique, taking the CFL number into account, is proposed to improve convergence and accuracy. A second order and first order discretization schemes of the advective and viscous terms respectively are applied. The advective upwinding is performed by the AUSM+up scheme. The latter is modified to achieve robustness and accuracy for all Mach and CFL numbers