Probabilistic Flux Limiters
Nga T.T. Nguyen-Fotiadis, Robert Chiodi, Michael McKerns, Daniel, Livescu, and Andrew Sornborger

TL;DR
This paper introduces a probabilistic flux limiter for shock capturing in fluid simulations, which accounts for uncertainty and randomness, outperforming traditional limiters in accuracy and adaptability.
Contribution
A novel probabilistic flux limiter framework that incorporates uncertainty and randomness, trained on high-resolution data, enhancing shock capturing performance.
Findings
Outperforms standard flux limiters in shock profile accuracy
Can be improved by expanding the set of flux limiting functions
Demonstrated using Burgers' equation as a test case
Abstract
The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters has been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Moreover, while aleatoric (inherent randomness) and epistemic (lack of knowledge) uncertainty is commonplace in fluid dynamical systems, these effects are generally ignored in the design of flux limiters. Even for deterministic dynamical models, numerical uncertainty is…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsParallel Computing and Optimization Techniques · Numerical Methods and Algorithms
MethodsSparse Evolutionary Training
