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Weakly compressible high-order I-stable central difference schemes for incompressible viscous flows

✍ Scribed by Weizhu Bao; Shi Jin

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
653 KB
Volume
190
Category
Article
ISSN
0045-7825

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✦ Synopsis

In this paper, we propose a weakly compressible model for numerical simulation of the incompressible viscous ¯ows. This model asymptotically approximates the incompressible Navier±Stokes equations when the mach number tends to zero. The main advantage of this model is that its numerical discretization avoids any Poisson solver, thus is very attractive for problems with complicated geometries. This model is discretized by high-order center dierences in space and the so-called `I-stable' method for time. The linear stability region of an I-stable method contains part of the imaginary axis. When solving a system of convection±diusion equations with a small viscosity, the I-stable method allows a very large cell Reynolds number, thus is particularly suitable for the simulation of ¯uid ¯ows with large Reynolds numbers. Numerical experiments illustrate the eciency and robustness of this approach.

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