Eulerian-Lagrangian methods for the Navier-Stokes equations at high Reynolds number

✍ Scribed by Vincenzo Casulli

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 681 KB
• Volume: 8
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650081016

✦ Synopsis

In this paper an explicit Lagrangian approach to advective and diffusive term treatment has been derived to improve the stability and to reduce the artificial diffusion of a finite difference scheme for convection-diffusion equations. This concept is then applied to discretize the convective and viscous terms in the Navier-Stokes equations. The pressure gradient and the velocity divergence are discretized by implicit finite differences in such a way that the resulting velocity field is exactly discrete divergence-free at all times. The stability of the method is shown to become less restrictive as the Reynolds number increases. At large time steps the artificial viscosity also reduces and higher accuracy is obtained. Moreover, the present algorithm is so devised as to take full advantage of vector computations in view of a possible implementation of it on an array computer. The performance of the method is illustrated by the numerical solution obtained for the cavity flow problem at high Reynolds numbers.