I am very happy to report on the following highlights recently achieved in developing new numerical models and methods for two-phase flow and transport processes at/on fluid interfaces using OpenFOAM® as a central C++ based development platform.
To the best of our knowledge, we are first in having the three main representatives for Direct Numerical Simulations (DNS) for two-phase flows on a single software platform, OpenFOAM®: Interface-Capturing, Interface-Tracking and Front-Tracking methods. This has involved the development and implementation of the geometrical Volume-of-Fluid Interface-Capturing method (voFoam) and the hybrid Level-Set Front-Tracking method (lentFoam) in the OpenFOAM® framework. Moreover, recently the Phase-Field method (phaseFieldFoam) has been implemented successfully using OpenFOAM® technology. With this portfolio including both sharp and diffuse interface approaches to discretely represent fluid interfaces, a vast variety of interfacial transport processes can be addressed in an appropriate(!) yet very flexible manner re-using the modular framework of OpenFOAM®.
Numerical methods for viscoelastic flow are known to suffer from stability problems at moderate and high measures of the fluid elasticity. The loss of convergence of all iterative algorithms beyond some limiting value of the fluid elasticity is well-known in Computational Rheology as the so-called 'High Weissenberg Number Problem' (HWNP). The HWNP for visoelastic flows is a persistent one in the field of Computational Rheology which has not been resolved for the last 40 years. We have developed a new comprehensive stabilization library using OpenFOAM® that contains cutting-edge stabilization approaches for high Weissenberg number flows. Our generic framework has been implemented in a way that provides full combinatorial flexibility between a comprehensive set of rheological models on the one hand and distinct stabilization approaches on the other hand. Our stabilization framework has been found to be both robust (convergent and stable) and accurate in viscoelastic benckmark testcases, while signicantly alleviating the HWNP. The stabilized method has demonstrated to converge up to a Weissenberg number of Wi = 100.
Direct Numerical Simulation of interfacial transport of surfactant mixtures on fluid interfaces (relevant to many industrial processes) is one example for complex interfacial multiphysics which usually imposes several challenges to the numerical method. Here, we have significantly enhanced OpenFOAM®'s interface tracking solver framework. To the best of our knowledge, we are first in having developed an accurate, convergent and conservative solution procedure, which uses a novel enhanced discretization scheme for diffusive transport on fluid interfaces and inherently takes into account the coupled nature of interfacial transport of multicomponent surfactants systems (i.e. so called cross effects between surfactant species) utilizing a block-coupled solution technique. Moreover, the solver framework has been accompanied by a comprehensive model library in order to account for virtually all types of sorption models, covering both the sorption-limited and the transport-limited cases. With this approach detailed and novel insights into the complex interplay of interface dynamics and interfacial transport of surfactants can be gained.
All projects have been accomplished using modern C++ programming techniques and design patterns within OpenFOAM®, a mature yet flexible open source C++ library for Computational Continuum Mechanics. Emphasis has been put on sustainability, maintainability as well as on performance and flexibility through the chosen software design patterns, adhering to the code style guide and documentation.