We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.

中文翻译：

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等熵两相流的全马赫数有限体积法

我们提出了一种在所有马赫数范围内的等熵两相流的隐式-显式有限体积方案。基础模型属于对称双曲线热力学兼容模型类。该方案的关键要素包括参考状态下的压力和焓项的线性化。由此产生的刚性线性部分被隐式集成，而非线性高阶和传输项被显式处理。由于通量分裂，该方案在 CFL 条件下是稳定的，该条件由慢物质波的分辨率决定，即使在存在快声波的情况下也允许大的时间步长。进一步研究了模型的奇异马赫数极限，证明了该方案的渐近保持性。