Crank-Nicolson Scheme for Solving Low Mach Number Unsteady Viscous Flows Using an Implicit Preconditioned Dual Time Stepping Technique

The aim of this paper is to simulate low Mach number unsteady viscous flows using a density-based finite volumes solver. This kind of solver is known to encounter some difficulties to simulate low Mach number flows in which the density is almost constant. Convergence fails or accuracy decreases when the speed of sound is much greater than the fluid velocity. Local preconditioning methods intend to solve this problem by altering the time derivative terms of the Navier-Stokes equations in order to artificially modify the speed of sound, improving the convergence and accuracy in the case of low Mach number steady flows.