Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries

Abstract

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.

arXiv comment34 pages, 18 figures, 4 tables

References in corpus (13)

• Recent progress and challenges in exploiting graphics processors in computational fluid dynamics
• A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability
• A diffuse interface model for two-phase ferrofluid flows
• An Interface-Tracking Technique for Multiphase Flow with Soluble Surfactant
• Confronting Grand Challenges in Environmental Fluid Mechanics
• MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver
• A CutFEM method for two-phase flow problems
• Automatic differentiation in ML: Where we are and where we should be going
• FluTAS: A GPU-accelerated finite difference code for multiphase flows
• Solving the Discretised Neutron Diffusion Equations using Neural Networks
• Performance portability of lattice Boltzmann methods for two-phase flows with phase change
• Solving the Discretised Boltzmann Transport Equations using Neural Networks: Applications in Neutron Transport
• Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics