Computation of statistical solutions of hyperbolic systems of conservation laws
Open access
Author
Date
2020Type
- Doctoral Thesis
ETH Bibliography
yes
Altmetrics
Abstract
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation laws. By combining high-resolution finite volume methods with a Monte Carlo sampling procedure, we present a numerical algorithm to approximate statistical solutions. Under verifiable assumptions on the finite volume method, we prove that the approximations, generated by the proposed algorithm, converge in an appropriate topology to a statistical solution. Numerical experiments illustrating the convergence theory and revealing interesting properties of statistical solutions, are also presented.
We furthermore show that the multi-level Monte Carlo algorithm converges in the weak topology, and provide testable conditions for when the multi-level Monte Carlo algorithm outperforms the Monte Carlo algorithm.
Finally we present the Alsvinn simulator, a fast multi general purpose graphical processing unit (GPGPU) finite volume solver for hyperbolic conservation laws in multiple space dimensions. Alsvinn has native support for uncertainty quantifications, and exhibits excellent scaling on top tier compute clusters. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000432014Publication status
publishedExternal links
Search print copy at ETH Library
Contributors
Examiner: Mishra, Siddhartha
Examiner: Fjordholm, Ulrik S.
Examiner: Chen, Gui-Qiang
Examiner: Szepessy, Anders
Publisher
ETH ZurichSubject
Uncertainty Quantification; Hyperbolic conservation laws; Monte Carlo simulation; high performance computingOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
More
Show all metadata
ETH Bibliography
yes
Altmetrics