论文标题
可压缩两相流的动能和熵保护方案
A kinetic energy--and entropy-preserving scheme for compressible two-phase flows
论文作者
论文摘要
可压缩流的准确数值建模，尤其是在湍流制度中，需要一种在高雷诺（$ re $ $）数字上是非疾病和稳定的方法。对于可压缩的流动，已经知道动能的离散保守性不是数值稳定性的足够条件，这与不可压缩的流动不同。 在这项研究中，我们采用了最近开发的保守漫射界面方法（Jain，mani $ \＆$ moin，$ \ textit {j。Comput。phys。phys。} $，2020），以及五个方程模型，用于模拟可压缩的两相流量。这种方法可离散地保存系统的每个阶段，动量和总能量的质量。我们在这里提出了数值通量之间的离散一致性条件，以使满足这些条件的任何数值通量都不会微不足道地有助于系统的动能和熵。我们还提供了一组数字通量\ textemdash，它满足了这些一致性条件\ textemdash，从而在没有压力工作，粘度，热扩散效应和时间消除误差的情况下，可以准确地保护动能和熵的近似保护。由于模型始终减少到单相纳维尔 - 斯托克斯系统时，当两个阶段的性质相同时，因此提出的一致性条件和数值通量也适用于更广泛的单相流。 为此，我们提出了无限$ re $下的可压缩单相和两相湍流的粗网格数值模拟，以说明在规范验证案例中所提出的方法的稳定性，例如各向同性湍流和泰勒式涡流流。还提出了对液滴可压缩衰减的较高分辨率模拟，并分析了液滴对流动的影响。
Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds ($Re$) numbers. For a compressible flow, it is known that discrete conservation of kinetic energy is not a sufficient condition for numerical stability, unlike in incompressible flows. In this study, we adopt the recently developed conservative diffuse-interface method (Jain, Mani $\&$ Moin, $\textit{J. Comput. Phys.}$, 2020) along with the five-equation model for the simulation of compressible two-phase flows. This method discretely conserves the mass of each phase, momentum, and total energy of the system. We here propose discrete consistency conditions between the numerical fluxes, such that any set of numerical fluxes that satisfy these conditions would not spuriously contribute to the kinetic energy and entropy of the system. We also present a set of numerical fluxes\textemdash which satisfies these consistency conditions\textemdash that results in an exact conservation of kinetic energy and approximate conservation of entropy in the absence of pressure work, viscosity, thermal diffusion effects, and time-discretization errors. Since the model consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical, the proposed consistency conditions and numerical fluxes are also applicable for a broader class of single-phase flows. To this end, we present coarse-grid numerical simulations of compressible single-phase and two-phase turbulent flows at infinite $Re$, to illustrate the stability of the proposed method in canonical test cases, such as an isotropic turbulence and Taylor-Green vortex flows. A higher-resolution simulation of a droplet-laden compressible decaying isotropic turbulence is also presented, and the effect of the presence of droplets on the flow is analyzed.
