Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

✍ Scribed by Y. Morinishi; T.S. Lund; O.V. Vasilyev; P. Moin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 451 KB
• Volume: 143
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1998.5962

✦ Synopsis

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass, momentum, and kinetic energy. This deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems. Finite difference schemes in a collocated grid system are also analyzed, and a violation of kinetic energy conservation is revealed. The predicted conservation properties are demonstrated numerically in simulations of inviscid white noise, performed in a two-dimensional periodic domain. The proposed fourth order schemes in a staggered grid system are generalized for the case of a nonuniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow.