Fully conservative higher order finite difference schemes for incompressible flow
Fully conservative higher order finite difference schemes for incompressible flow
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DOI：
10.1006/jcph.1998.5962
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发表时间：
1998-06-10
影响因子：
4.1
通讯作者：
Moin, P
中科院分区：
文献类型：
--
作者：
Morinishi, Y;Lund, TS;Moin, P
不可压缩流的质量、动量和动能方程的守恒性质被指定为一组适当的离散方程的分析要求。检查规则和交错网格系统中现有的有限差分方案是否违反守恒要求，并指出一些重要的差异。特别是，我们发现现有的交错网格系统的高阶方案都不能同时守恒质量、动量和动能。通过推导交错网格系统的完全保守的高阶精确有限差分格式的一般族，可以纠正此缺陷。还分析了并置网格系统中的有限差分格式，并揭示了动能守恒定律的违反。预测的守恒特性在二维周期域中进行的无粘性白噪声模拟中得到了数值证明。所提出的交错网格系统中的四阶方案被推广到非均匀网格的情况，并且所得方案用于执行湍流通道流的大涡模拟。 (C) 1998 年学术出版社。
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 non uniform mesh, and the resulting scheme is used to perform large eddy simulations of turbulent channel flow. (C) 1998 Academic Press.