Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Harmon, Jake J.; Tokareva, Svetlana; Zlotnik, Anatoly; Swart, Pieter J.

doi:10.1137/23m1624750

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Journal Article · Wed Apr 02 00:00:00 EDT 2025 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/23m1624750· OSTI ID:2556812

^[1]; Tokareva, Svetlana ^[1]; Zlotnik, Anatoly ^[1]; Swart, Pieter J. ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2556812

Report Number(s):: LA-UR--24-30309

Journal Information:: SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 2 Vol. 13; ISSN 2166-2525

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

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