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A relaxation method for two-phase flow models with hydrodynamic closure law

机译：具有流体动力闭合律的两相流模型的松弛方法

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摘要

This paper is devoted to the numerical approximation of the solutions of a system of conservation laws arising in the modeling of two-phase flows in pipelines. The PDEs are closed by two highly nonlinear algebraic relations, namely, a pressure law and a hydrodynamic one. The severe nonlinearities encoded in these laws make the classical approximate Riemann solvers virtually intractable at a reasonable cost of evaluation. We propose a strategy for relaxing solely these two nonlinearities. The relaxation system we introduce is of course hyperbolic but all associated eigenfields are linearly degenerate. Such a property not only makes it trivial to solve the Riemann problem but also enables us to enforce some further stability requirements, in addition to those coming from a Chapman-Enskog analysis. The new method turns out to be fairly simple and robust while achieving desirable positivity properties on the density and the mass fractions. Extensive numerical evidences are provided.
机译：本文致力于在管道两相流建模中产生的守恒律系统解的数值近似。 PDE由两个高度非线性的代数关系封闭，即压力定律和流体动力学定律。这些定律中编码的严重非线性使经典的近似Riemann求解器在合理的评估成本下几乎难以处理。我们提出了仅放松这两个非线性的策略。我们介绍的松弛系统当然是双曲的，但是所有相关的本征场都是线性退化的。除了Chapman-Enskog分析得出的那些要求外，这种特性不仅使解决黎曼问题变得轻而易举，而且使我们能够执行一些进一步的稳定性要求。事实证明，该新方法相当简单且健壮，同时在密度和质量分数上实现了理想的正性。提供了大量的数字证据。

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