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

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

Vigneron, D.
Deliége, G.
Essers, J.A.

2006-09-05

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.

unsteady viscous flows
implicit methods
local preconditioning techniques
AUSM+up scheme
low Mach number flows

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Conference proceedings

conference paper

(c) 2006 Vigneron, D.; Deliége, G.; Essers, J.A.