Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations

A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is sati...

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Bibliographic Details
Published in:Journal of computational physics 2004-07, Vol.197 (2), p.686-710
Main Authors: Morinishi, Youhei, Vasilyev, Oleg V., Ogi, Takeshi
Format: Article
Language:English
Subjects:
Computational techniques
Concentric annuli flow
Conservation properties
Cylindrical coordinate
DNS
Energy conservation
Exact sciences and technology
Finite difference scheme
LES
Mathematical methods in physics
Non-uniform gird
Physics
Pipe flow
Pole treatment
Staggered grid
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Summary:A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied. A novel pole treatment is also introduced, where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole. The pole singularity is removed properly using analytical and numerical techniques. The kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates. The pole treatment is verified for inviscid pipe flow. Mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2003.12.015