Statistical solutions of hyperbolic systems of conservation laws: numerical approximation
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.
Keywords
Cite
@article{arxiv.1906.02536,
title = {Statistical solutions of hyperbolic systems of conservation laws: numerical approximation},
author = {Ulrik Skre Fjordholm and Kjetil Lye and Siddhartha Mishra and Franziska Weber},
journal= {arXiv preprint arXiv:1906.02536},
year = {2024}
}