Consistent and symmetry preserving data-driven interface reconstruction for the level-set method

Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics (CFD) solvers, e.g., the cell face reconstruction in the finite-volume method or the curvature computation in the Volume-of-Fluid (VOF) method. The latter showed improvements in terms of accuracy for coarsely resolved interfaces, however at the expense of convergence and symmetry. In this work, a hybrid data-driven approach is proposed, addressing the aforementioned shortcomings. We focus on interface reconstruction (IR) in the level-set method, i.e., the computation of the volume fraction and apertures. In the hybrid data-driven IR, a classification neural network decides based on the local interface resolution whether to use conventional linear IR or neural network IR. The proposed approach improves accuracy for coarsely resolved interfaces and recovers the conventional IR for high resolutions, yielding first order overall convergence. Symmetry is preserved by mirroring and rotating the input level-set grid and subsequently averaging the predictions. The hybrid model is implemented into a CFD solver and demonstrated for two-phase flows. Furthermore, we provide details of floating-point symmetric implementation and computational efficiency.