FULLY CONSERVATIVE HIGHER-ORDER FINITE-DIFFERENCE SCHEMES FOR INCOMPRESSIBLE-FLOW

Conservation properties of the mass, momentum, and kinetic energy equa tions for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference sc hemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies ar e pointed out. In particular, it is found that none of the existing hi gher order schemes for a staggered mesh system simultaneously conserve mass, momentum, and kinetic energy. This deficiency is corrected thro ugh the derivation of a general family of fully conservative higher or der accurate finite difference schemes for staggered grid systems. Fin ite difference schemes in a collocated grid system are also analyzed, and a violation of kinetic energy conservation is revealed. The predic ted conservation properties are demonstrated numerically in simulation s of inviscid white noise, performed in a two-dimensional periodic dom ain, The proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh, and the resulting sche me is used to perform large eddy simulations of turbulent channel flow . (C) 1998 Academic Press.