Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics is neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases.

中文翻译：

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一种低马赫数液-气流动的界面捕获方法

多相、可压缩和粘性流动在广泛的科学和工程问题中至关重要。尽管在过去的几十年里付出了巨大的努力来开发准确有效的数值技术来解决这类问题，但当前的模型需要进一步改进以解决实际应用问题。在这种情况下，我们提出了一种模拟多相粘性流动的数值方法，其中可压缩和不可压缩相在低马赫数状态下相互作用。在该框架中，声学被忽略，但可压缩相的大密度变化以及传热、对流和扩散过程都可以考虑在内。该问题在利用 Navier-Stokes 方程的低马赫数渐近展开的完全欧拉框架中得到解决。流体体积法 (VOF) 用于捕获液-气界面，建立在大规模并行求解器之上，在时间和空间上均具有二阶精度。隐式处理二阶压力项，并使用本征展开方法求解所得压力方程，该方法采用稳健且新颖的公式。我们提供了理论方法的详细而完整的描述以及有关数值技术和实现细节的信息。提供了五个不同测试用例的基准测试结果。隐式处理二阶压力项，并使用本征展开方法求解所得压力方程，该方法采用稳健且新颖的公式。我们提供了理论方法的详细而完整的描述以及有关数值技术和实现细节的信息。提供了五个不同测试用例的基准测试结果。隐式处理二阶压力项，并使用本征展开方法求解所得压力方程，该方法采用稳健且新颖的公式。我们提供了理论方法的详细而完整的描述以及有关数值技术和实现细节的信息。提供了五个不同测试用例的基准测试结果。