A sharp interface finite volume method for variable density zero Mach number two-phase flow with surfactant-dependent surface tension

许多重要的工业化学过程和自然现象都可以用变密度零马赫数两相流方程来描述，两相流通过分离两种流体的界面进行传热和传质。建模和模拟此类流动的一些主要挑战来自于压力、密度和浓度的不连续分布，来自于流体性质（如粘度、扩散率或电导率）在相边界上的大比例，以及来自于在运动表面上求解物质输运方程的必要性。本研究项目的重点是研究零马赫数两相流的局部二阶精确有限体积法的设计，该方法具有可溶表面活性剂和非混相界面上的传质。在前期工作的基础上，重点解决以下问题：i)设计了具有不连续点显式表示的笛卡尔网格上的保守尖锐界面有限体积投影方法，ii)开发了表面活性剂方程的保守有限体积离散化方法，以及iii)实现了具有任意大系数比的界面问题的变系数泊松投影方程的基于渐近的有效解策略。该项目有助于优先计划的目标，即发展“解决界面局部过程的多相流问题的数值模拟方法”。

Many important industrial chemical processes and naturally occurring phenomena can be described by the equations for variable density zero Mach number two-phase flow with heat and mass transfer across an interface separating the two fluids. Some of the main challenges in modeling and simulating such flows result from discontinuous distributions of pressure, density, and concentrations, from large ratios of fluid properties, such as viscosity, diffusivity, or conductivity, across the phase boundaries, and from the necessity of solving species transport equations on the moving surfaces. This research project focuses on the proper design of a locally second order accurate finite volume method for zero Mach number two-phase flow with soluble surfactants and mass transfer across an immiscible interface. Based on our previous work we specifically address the following issues: i) design of a conservative sharp interface finite volume projection method on Cartesian grids with explicit representation of discontinuities, ii) development of a conservative finite volume discretisation of surface surfactant equations, and iii) implementation of an asymptotics based efficient solution strategy for the variable coefficient Poisson projection equation for interface problems with arbitrarily large ratio of the coefficients. The project contributes to the Priority Program’s goal of developing “numerical methods for the simulation of multiphase flow problems which resolve the local processes at the interface.”