A six-point neuron-based ENO (NENO6) scheme for compressible fluid dynamics

TL;DR

This paper introduces a neural network-based ENO scheme (NENO6) that improves discontinuity detection and reconstruction in compressible fluid dynamics, demonstrating enhanced robustness and accuracy over existing methods.

Contribution

A novel neural network-driven ENO scheme (NENO6) that replaces classical smoothness indicators with an ANN for stencil selection, improving robustness and generality.

Findings

Outperforms WENO-CU6 and TENO6-opt schemes in benchmark tests.

Demonstrates high fidelity in discontinuity detection.

Applicable to 1D and 2D conservation law problems.

Abstract

In this work, we introduce a deep artificial neural network (ANN) that can detect locations of discontinuity and build a six-point ENO-type scheme based on a set of smooth and discontinuous training data. While a set of candidate stencils of incremental width is constructed, the ANN instead of a classical smoothness indicator is deployed for an ENO-like sub-stencil selection. A convex combination of the candidate fluxes with the re-normalized linear weights forms the six-point neuron-based ENO (NENO6) scheme. The present methodology is inspired by the work [Fu et al., Journal of Computational Physics 305 (2016): 333-359] where contributions of candidate stencils containing discontinuities are removed from the final reconstruction stencil. The binary candidate stencil classification is performed by a well-trained ANN with high fidelity. The proposed framework shows an improved generality and robustness compared with other ANN-based schemes. The generality and performance of the proposed NENO6 scheme are demonstrated by examining one- and two-dimensional benchmark cases with different governing conservation laws and comparing to those of WENO-CU6 and TENO6-opt schemes.