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Fully conservative higher order finite difference schemes for incompressible flow. (English) Zbl 0932.76054
Summary: 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 on 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 on collocated grid systems 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 on staggered grid system are generalized for the case of a non-uniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow. \(\copyright\) Academic Press.

76M20 Finite difference methods applied to problems in fluid mechanics
76D99 Incompressible viscous fluids
76F65 Direct numerical and large eddy simulation of turbulence
Full Text: DOI
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