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

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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.”