A consistent methodology to transport a passive scalar with the geometric Volume-of-Fluid method isoAdvector

This paper presents a new methodology allowing the discretisation of phase specific transport equations within the Volume-of-Fluid interface capturing method framework. The method uses a sharp interface algorithm to compute the transport of species concentration. The interface reconstruction and advection is provided by the geometric advection scheme isoAdvector [1] implemented in the OpenFOAM® library. When discretising the transport equation for species, lack of consistency with the free surface advection scheme can lead to numerical errors, causing conservation or boundedness issues. This work addresses the issue of consistency in convective transport of species and is divided in two parts. First, a new interpolation procedure is used to compute face values from cell-centered values. Then, the diffusive operator of the transport equation is corrected. Finally, a set of test cases are presented to validate the transport equation's consistency with the free surface advection. Species transport across the interface is not part of the scope of this article, however, this methodology can further be used to study mass transfer at the gas-liquid interface using additional mass source terms that are not discussed here.