Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows
Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows
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DOI：
10.1006/jcph.1999.6408
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发表时间：
2000-02
影响因子：
4.1
通讯作者：
F. Nicoud
中科院分区：
文献类型：
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作者：
F. Nicoud
提出了三种有限差分算法来求解纳维斯托克斯方程的低马赫数近似。这些算法表现出四阶空间精度和二阶时间精度。它们是无耗散的，因此非常适合湍流的 DNS 和 LES。所提出的每种方法的共同关键要素是具有可变系数的泊松方程，可求解流体动压。此功能可确保速度场受到正确约束。结果表明，需要这种方法来避免违反无粘极限中的动能守恒，否则动量方程中的压力项会出现违反动能守恒的情况。一组现有的不可压缩流动的有限差分公式被推广为处理任意大的密度波动，而不会违反非线性对流项的守恒。当使用近似状态方程而不是精确状态方程时，可以获得一种完全守恒质量、动量和动能的算法。模型问题的结果用于显示空间和时间收敛速度，并提供了几个测试用例来说明算法的性能。
Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier?Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite-difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non-linear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.