This paper is devoted to the simulation of the three-phase flow model [20], in order to account for immiscible components. The whole model is first recalled, and the main properties of the closed set are given, with particular focus on the Riemann problem associated with the convective subset that contains non-conservative terms, and also on the relaxation process. The model is hyperbolic, far from resonance occurrence, and a physically relevant entropy inequality holds for smooth solutions of the whole system. Owing to the uniqueness of jump conditions, specific solutions of the one-dimensional Riemann problem can be built, and these are useful (and mandatory) for the verification procedure. The fractional step method proposed herein complies with the continuous entropy inequality, and implicit schemes that are considered to account for relaxation terms take their roots on the true relaxation process. Once verification tests have been achieved, focus is given on the simulation of the experimental setup [8, 9], in order to simulate a cloud of droplets that is hit by an incoming gas shock-wave. Finally, the study of a three-phase flow setup involving thermal effects is presented, it is based on the KROTOS experiment [25] which focuses on vapour explosion simulation.

本文致力于模拟三相流模型[20]，以解决不溶混组分的问题。首先回顾整个模型，并给出封闭集的主要性质，特别关注与包含非保守项的对流子集相关的黎曼问题，以及松弛过程。该模型是双曲线的，没有共振发生，并且在物理上相关的熵不等式适用于整个系统的平滑解。由于跳跃条件的独特性，可以建立一维Riemann问题的特定解决方案，它们对于验证过程很有用（和强制性）。本文提出的分数步法符合连续熵不等式，而被认为是解释松弛项的隐式方案则源于真正的松弛过程。一旦完成验证测试，就将重点放在实验装置的仿真上[8，9]，以便模拟被入射气体冲击波撞击的液滴云。最后，基于KROTOS实验[25]，该实验研究了涉及热效应的三相流装置，该实验侧重于蒸气爆炸模拟。