Purpose

The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.

Design/methodology/approach

The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.

Findings

The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.

Originality/value

While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

中文翻译：

---

非平衡两相流方程的高阶松弛方法

目的

本文的目的是研究涉及气液混合物的两相流问题。

设计/方法论/途径

受控方程由一系列守恒定律组成，对气液混合物速度非平衡条件下的两相流现象的分类进行建模。在本模型中，相对速度的影响通过与控制气相质量和体积分数的特定方程组耦合的动力学本构关系来解释。与许多两相模型不同，所考虑的系统是完全双曲线且完全保守的。建议的松弛方法将非线性双曲系统转换为包含源松弛项和特征线性属性的半线性模型。值得注意的是，该模型可以在不使用黎曼求解器或线性迭代的情况下进行数值求解。为了实现精确的时间积分，使用高分辨率空间重建和总变差递减的龙格-库塔方案来离散松弛系统。

发现

该方法用于解决各种非平衡两相流问题，并对不同的重建进行比较研究。数值结果证明了所建议的松弛方法的高分辨率能力，证实了其对以强冲击为特征的流态进行精确模拟的能力。

原创性/价值

虽然松弛方法表现出显着的性能和竞争特征，但据我们所知，还没有尝试使用这些方法来解决非平衡两相流问题。