RiemannONets: Interpretable Neural Operators for Riemann Problems

arXiv:2401.08886v2 Announce Type: replace
Abstract: Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve Riemann problems encountered in compressible flows for extreme pressure jumps (up to $10^{10}$ pressure ratio). In particular, we first consider the DeepONet that we train in a two-stage process, following the recent work of \cite{lee2023training}, wherein the first stage, a basis is extracted from …

arxiv cs.lg operators physics.flu-dyn type