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

TL;DR

This paper introduces a symmetry-preserving deep learning approach for accurately estimating interface curvature in volume of fluid simulations, maintaining symmetry invariance and improving performance over traditional methods.

Contribution

It presents a novel neural network architecture that conserves interface symmetries, ensuring consistent results across different grid resolutions in VOF methods.

Findings

Outperforms conventional curvature estimation schemes.

Maintains accuracy and convergence with smaller computational stencils.

Demonstrates robustness across various grid refinements.

Abstract

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform conventional methods on coarser grids but diverge with grid refinement. Furthermore, unlike conventional methods, data-driven methods are sensitive to coordinate system and sign conventions, thus often fail to capture basic symmetry patterns in interfaces. The present work proposes a new data-driven strategy which conserves the symmetries in a cost-effective way and delivers consistent results over a wide range of grids. The method is based on artificial neural networks with deep multilayer perceptron (MLP) architecture which read volume fraction fields on regular grids. The anti-symmetries are preserved with no additional cost by employing a neural network model with input normalization, odd-symmetric activation functions and bias-free neurons. The symmetries are further conserved by height-function inspired rotations and averaging over several different orientations. The new symmetry-preserving MLP model is implemented into a flow solver (OpenFOAM) and tested against conventional schemes in the literature. It shows superior performance compared to its standard counterpart and has similar accuracy and convergence properties with the state-of-the-art conventional method despite using smaller stencil.