Fully conservative higher order finite difference schemes for incompressible flow.

*(English)*Zbl 0932.76054Summary: 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.

##### MSC:

76M20 | Finite difference methods applied to problems in fluid mechanics |

76D99 | Incompressible viscous fluids |

76F65 | Direct numerical and large eddy simulation of turbulence |

##### Keywords:

regular grid systems; staggered grid systems; collocated grid systems; inviscid white noise; two-dimensional periodic domain; non-uniform mesh; large eddy simulations; turbulent channel flow
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\textit{Y. Morinishi} et al., J. Comput. Phys. 143, No. 1, 90--124 (1998; Zbl 0932.76054)

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