Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows
Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows
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DOI：
10.1016/j.jcp.2009.09.021
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发表时间：
2010-01-20
影响因子：
4.1
通讯作者：
Morinishi, Yohei
中科院分区：
文献类型：
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作者：
Morinishi, Yohei
Morinishi等[Y. Morinishi，T.S.隆德，O.V. Vasilyev，P. Moin，不可压缩流的完全守恒高阶有限差分格式，J. Comput. Phys.124（1998）90]，并提出了适用于无激波非定常可压缩流模拟的全守恒有限差分格式。对流项的可交换发散、平流和斜对称形式通过包括可压缩流的时间导数项来定义。如果满足连续性，则这些形式在解析上是等价的，反对称形式在没有连续性的情况下是次保守的，而发散形式是主保守的。本文还揭示了现有拟反对称形式与现有拟反对称形式之间的关系。然后在交错网格系统中导出对流问题的可交换全离散有限差分格式，只要满足相应的离散连续性，它们是完全守恒的。此外，基于反对称格式，提出了一种适用于紧致差分格式的半离散对流格式。在三维周期性无粘流场中数值模拟了该格式的守恒性质。本文还将所提出的全离散全守恒二阶精度格式用于可压缩各向同性湍流的数值模拟和开腔流动的数值模拟。(C)2009 Elsevier Inc. All rights reserved.
The form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Morinishi et al. [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 124 (1998) 90], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow. These forms are analytically equivalent if the continuity is satisfied, and the skew-symmetric form is secondary conservative without the aid of the continuity, while the divergence form is primary conservative. The relations between the present and existing quasi-skew-symmetric forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-symmetric form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow. (C) 2009 Elsevier Inc. All rights reserved.