Statistical solutions of hyperbolic systems of conservation laws: Numerical approximation
- Fjordholm, U. S. Department of Mathematics, University of Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
- Lye, K. Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
- Mishra, S. Seminar for Applied Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
- Weber, F. Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA
- 2020-3-20
Published in:
- Mathematical Models and Methods in Applied Sciences. - World Scientific Pub Co Pte Lt. - 2020, vol. 30, no. 03, p. 539-609
English
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which 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.
- Language
-
- English
- Open access status
- green
- Identifiers
-
- DOI 10.1142/s0218202520500141
- ISSN 0218-2025
- Persistent URL
- https://sonar.ch/global/documents/267787
Statistics
Document views: 11
File downloads:
- Full-text: 0