A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction

TL;DR

This paper introduces a novel 3D volume of fluid method using machine learning that predicts flux fractions without explicit interface reconstruction, improving accuracy and efficiency in multi-material flow simulations.

Contribution

The method employs a trained neural network to compute fluxes directly, eliminating the need for explicit interface reconstruction in 3D multi-material flow simulations.

Findings

Numerical convergence observed as mesh size decreases.

Better convergence rate than two reference schemes.

Method effectively handles complex interface geometries.

Abstract

We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains. One of the novelties of the method is that the flux fraction is computed by evaluating a previously trained neural network and without explicitly reconstructing any local interface approximating the exact one. The network is trained on a purely synthetic dataset generated by randomly sampling numerous local interfaces and which can be adapted to improve the scheme on less regular interfaces when needed. Several strategies to ensure the efficiency of the method and the satisfaction of physical constraints and properties are suggested and formalized. Numerical results on the advection equation are provided to show the performance of the method. We observe numerical convergence as the size of the mesh tends to zero $h=1/N_h\searrow 0$, with a better rate than two reference schemes.