This paper presents a cell-centered high order finite volume scheme for the solution of the three-dimensional (3D) Navier-Stokes equations with low Mach number. The system of non-linear equations is solved by means of a fully implicit pseudo-transient scheme. Each pseudo-time step is solved by a Newton-GMRes procedure. A local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low Mach number and low cell Reynolds number. This preconditioning is applied to the AUSM+up flux vector splitting function. The method is tested on 2D and 3D low Mach number laminar flows. © 2007 Elsevier B.V. All rights reserved.
Vigneron, D., Vaassen, J. M., & Essers, J. A. (2008). An implicit finite volume method for the solution of 3D low Mach number viscous flows using a local preconditioning technique. Journal of Computational and Applied Mathematics, 215(2), 610–617. https://doi.org/10.1016/j.cam.2006.04.068