Stability investigation of a difference scheme for incompressible Navier-Stokes equations

Authors:
Dmytro Chibisov;Victor Ganzha;Ernst W. Mayr;Evgenii V. Vorozhtsov
Affiliations:
Institute of Informatics, Technische Universität München, Germany;Institute of Informatics, Technische Universität München, Germany;Institute of Informatics, Technische Universität München, Germany;Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Russia
Venue:
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Year:
2007

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Abstract

We investigate the stability of the modified difference scheme of Kim and Moin for numerical integration of two-dimensional incompressible Navier-Stokes equations by the Fourier method and by the method of discrete perturbations. The obtained analytic-form stability condition gives the maximum time steps allowed by stability, which are by factors from 2 to 58 higher than the steps obtained from previous empirical stability conditions. The stability criteria derived with the aid of CAS Mathematica are verified by numerical solution of two test problems one of which has a closed-form analytic solution.