The volume of fluid (VOF) method is a popular technique for the direct numerical simulations of flows involving immiscible fluids. A discrete volume fraction field evolving in time represents the interface, in particular, to compute its geometric properties. The height function method (HF) is based on the volume fraction field, and its estimate of the interface curvature converges with second-order accuracy with grid refinement. Data-driven methods have been recently proposed as an alternative to computing the curvature, with particular consideration for a well-balanced input data set generation and symmetry preservation. In the present work, a two-layer feed-forward neural network is trained on an input data set generated from the height function data instead of the volume fraction field. The symmetries for rotations, reflections, and the anti-symmetry for the phase swapping have been considered to reduce the number of input parameters. The neural network, establishing a correlation between curvature and height function values, can efficiently predict the local interface curvature. We compare the trained neural network to the standard Height Function method to assess its performance and robustness.

This paper investigates a numerical code coupling technique to tackle multi-physics and multi-scale simulations using state-of-the-art software packages that typically address some specific modeling domain. The coupling considers the in-house FEM code, FEMuS, and the FVM code OpenFOAM, by exploiting the MED library from the SALOME platform. The present approach is tested on a buoyancy-driven fluid flow within a square cavity, where the buoyancy force constitutes the coupling term. In uncoupled scenarios, momentum and temperature equations are solved both in FEM and FVM codes without data exchange. In the coupled setting, only the OpenFOAM velocity and the FEMuS temperature fields are solved separately and shared at each time step (or vice versa). The MED library handles the coupling with the addition of suitable ad-hoc data structures that perform the field transfer between codes. Different Rayleigh numbers are investigated, comparing the outcomes of coupled and uncoupled cases with reference literature results. Additionally, a boundary data transfer application is presented to extend the capabilities of the coupling algorithm to coupled applications with separate domains. In this problem, the two domains share interfaces and boundary values on specific fields as fluxes are exchanged between the two numerical codes.