Weakly compressible and advection approximations of incompressible viscous flows

We propose a simple and efficient method for numerical solution of weakly compressible approximation of incompressible viscous flows. Applying a low-Mach asymptotic in the compressible fluid problem, we derive a model which is capable to asymptotically capture the flow structures of the incompressible Navier-Stokes problem when the Mach number tends to zero. To solve numerically this model we combine a characteristic-based discretization with an explicit Runge-Kutta scheme with variable stability regions. The combined method is unconditionally stable. In addition, the restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in our algorithm. The performance of the method is illustrated by the driven cavity and the backward face step flows. Copyright (c) 2006 John Wiley & Sons, Ltd.