Numerical solution of the Navier--Stokes equations at high Reynolds numbers

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1974

DOI:https://doi.org/10.2172/4145043· OSTI ID:4145043

Shestakov, Aleksei Ilyich ^[1]

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1. Univ. of California, Davis, CA (United States)

A numerical method is presented which is designed to solve the Navier- Stokes equations for two-dimensional, incompressible flow. The method is intended for use on problems with high Reynolds numbers for which calculations via finite difference methods have been unattainable or unreliable. The proposed scheme is a hybrid utilizing a time-splitting finite difference method in areas away from the boundaries. In areas neighboring the boundaries, the equations of motion are solved by the newly proposed vortex method by Chorin. The major accomplishment of the new scheme is that it contains a simple way for merging the two methods at the interface of the two subdomains. The proposed algorithm is designed for use on the time-dependent equations but can be used on steady state problems as well. The method is tested on the popular, time-independent, square cavity problem, an example of a separated flow with closed streamlines. Numerical results are presented for a Reynolds number of 10³.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• DOE Contract Number: W-7405-ENG-48
• NSA Number: NSA-33-000540
• OSTI ID: 4145043
• Report Number(s): UCRL--51894
• Country of Publication: United States
• Language: English

Related Subjects

*INCOMPRESSIBLE FLOW-- EQUATIONS OF MOTION
*NAVIER-STOKES EQUATION-- NUMERICAL SOLUTION
420400* --Engineering--Heat Transfer & Fluid Flow
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
FINITE DIFFERENCE METHOD
N42300* --Engineering--Heat Transfer & Fluid Flow
REYNOLDS NUMBER