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arXiv 2109.01595physics.flu-dynphysics.comp-ph
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一种用于大密度比两相流的非结构化有限体积水平集/锋面追踪方法

An unstructured finite-volume level set / front tracking method for two-phase flows with large density-ratios

Jun Liu, Tobias Tolle, Dieter Bothe, Tomislav Maric

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AI总结：

本文扩展LENT方法至大密度比两相流，通过质量通量一致性实现数值稳定，适用于多种流体配对及强相互作用场景。

摘要：

我们通过为同位有限体积离散化单场两相Navier-Stokes方程中质量与动量守恒之间的数值一致性提供理论基础，扩展了非结构化水平集/锋面追踪（LENT）方法，以处理密度差异显著（高密度比）的两相流。我们的分析为Ghods和Herrmann [3]引入并在[4, 5, 6, 7, 8]中使用的质量守恒方程提供了理论基础。我们使用与两相动量对流项的隐式有限体积离散化中质量守恒一致的质量通量，并通过我们的SAAMPLE分离求解算法[2]求解单场Navier-Stokes方程。所提出的ρLENT方法在密度比范围为[1, 10^4]时，对球形液滴的两相动量平流恢复了精确的数值稳定性。数值稳定性通过相对L∞速度误差范数得到验证，适用于密度比在[1, 10^4]范围内、动态粘度比在[1, 10^4]范围内以及非常强的表面张力作用下的情况，包括具有挑战性的汞/空气和水/空气流体配对。此外，该求解器在强两相相互作用的情况下（如振荡液滴和上升气泡）表现良好。所提出的ρLENT方法适用于任何其他使用同位非结构化有限体积法离散化单场两相Navier-Stokes方程但不采用基于通量方法求解相指示器平流方程的两相流模拟方法，只需将所提出的质量通量几何近似和辅助质量守恒方程添加到求解算法中即可。

英文摘要：

We extend the unstructured LEvel set / froNT tracking (LENT) method for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and momentum conservation in the collocated Finite Volume discretization of the single-field two-phase Navier-Stokes equations. Our analysis provides the theoretical basis for the mass conservation equation introduced by Ghods and Herrmann [3] and used in [4, 5, 6, 7, 8]. We use a mass flux that is consistent with mass conservation in the implicit Finite Volume discretization of the two-phase momentum convection term, and solve the single-field Navier-Stokes equations with our SAAMPLE segregated solution algorithm [2]. The proposed $ρ$LENT method recovers exact numerical stability for the two-phase momentum advection of a spherical droplet with density ratios ranging in $[1, 10^4]$. Numerical stability is demonstrated for in terms of the relative $L_\infty$ velocity error norm, for density-ratios in the range of $[1, 10^4]$, dynamic viscosity-ratios in the range of $[1, 10^4]$ and very strong surface tension forces, for challenging mercury/air and water/air fluid pairings. In addition, the solver performs well in cases characterized by strong interaction between two phases, i.e., oscillating droplets and rising bubbles. The proposed $ρ$LENT method is applicable to any other two-phase flow simulation method that discretizes the single-field two-phase Navier-Stokes Equations using the collocated unstructured Finite Volume Method but does not solve an advection equation for the phase indicator using a flux-based approach, by adding the proposed geometrical approximation of the mass flux and the auxiliary mass conservation equation to the solution algorithm.

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