A low-dissipation reconstruction scheme for compressible single- and multi-phase flows based on artificial neural networks

TL;DR

This paper introduces a neural network-based reconstruction scheme for compressible flows that reduces numerical dissipation and computational cost while maintaining high accuracy in capturing complex flow structures.

Contribution

It presents a novel deepMTBVD scheme combining neural networks with BVD methods for efficient, low-dissipation simulations of single- and multi-phase compressible flows.

Findings

Reduces computational time by up to 40%.

Maintains accuracy comparable to existing schemes.

Effectively captures shock waves, interfaces, and vortices.

Abstract

Solving compressible flows containing both smooth and discontinuous flow structures remains a significant challenge for finite volume methods. Godunov-type finite volume methods are commonly used for numerical simulations of compressible flows. One of the key factors in obtaining high-quality solutions is high-fidelity spatial reconstruction. In this work, we introduce a new paradigm for constructing high-resolution hybrid reconstruction schemes for compressible flows. This approach generates training data based on BVD schemes for supervised learning and employs ANN to create an indicator that pre-selects the most suitable reconstruction scheme for each cell, achieving the lowest global numerical dissipation. The numerical schemes under this paradigm are more computationally efficient than similar schemes within the BVD framework, as each cell only requires constructing a single interpolation function. Following this paradigm, a novel low-dissipation reconstruction scheme based on the MUSCL-THINC-BVD scheme, named the deepMTBVD scheme, is proposed for compressible single- and multi-phase flows. The performance of the proposed scheme has been extensively verified through benchmark tests of single- and multi-phase compressible flows, where discontinuous and vortical flow structures, like shock waves, contact discontinuities, and material interfaces, as well as vortices and shear instabilities of different scales, coexist simultaneously. Numerical results indicate that the new deepMTBVD scheme performs as well as the original MUSCL-THINC-BVD scheme for numerical simulations of compressible flows while reducing computational time by up to 40%.