Stability of a colocated finite volume scheme for the incompressible Navier-Stokes equations

2007/04/05 by Zimmermann, Sebastien
#76B99 #76M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0704.0772

Abstract

We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are both piecewise constant (colocated scheme). We use a projection (fractional-step) method to deal with the incompressibility constraint. We prove that the differential operators in the Navier-Stokes equations and their discrete counterparts share similar properties. In particular, we state an inf-sup (Babuska-Brezzi) condition. We infer from it the stability of the scheme.

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