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

Abstract

Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers 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 combined approach is proposed, adressing the aforementioned shortcomings. We focus on interface reconstruction (IR) in the level-set method, i.e. the computation of the volume fraction and apertures. The combined model consists of a classification neural network, that chooses between the conventional (linear) IR and the neural network IR depending on the local interface resolution. 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 combined 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.

Deep learning of interfacial curvature: a symmetry-preserving approach for the volume of fluid method

“…figure 2. Small 3 × 3 stencil has been the standard choice for machine learning models [30,32,34,35,39]. The stencil configuration determines the dimension of the input layer, i.e., N i = 3 × 3 = 9.…”