On the Stability of Godunov-Projection Methods for Incompressible Flow

✍ Scribed by Michael L. Minion

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 491 KB
• Volume: 123
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0035

✦ Synopsis

been proposed for an increasingly wide range of problems including variable density flow , reacting flow in the zero An analysis of the stability of certain numerical methods for the linear advection-diffusion equation in two dimensions is per-Mach number limit , and incompressible flow on locally formed. The advection-diffusion equation is studied because it is refined meshes . In each of the above papers, the claim a linearized version of the Navier-Stokes equations, the evolution is made that the condition for stability of the overall method equation for density in Boussinesq flows, and a simplified form is essentially the advective CFL condition of the equations for bulk thermodynamic temperature and mass fraction in reacting flows. It is found that various methods currently in use which are based on a Crank-Nicholson type temporal discreti-u⌬t/h Յ 1 and v⌬t/h Յ 1,

(1)

zation utilizing second-order Godunov methods for explicitly calculating advective terms suffer from a time-step restriction which de-

where u and v are the horizontal and vertical velocity pends on the coefficients of diffusive terms. A simple modification in the computation of the advective derivatives results in a method components and h is the grid spacing. This condition is with a stability condition that is independent of the magnitude of used regardless of the magnitude of the viscosity.

the coefficients of the diffusive terms.