Statistical solutions of hyperbolic systems of conservation laws: numerical approximation

Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra, Franziska Weber
6/6/2019
math.NAphysics.flu-dyn

Official code: kjetil-lye/statistical_systems_paper_experiments (3 stars, MIT, last commit 2022-11-22). 1 more implementation below.

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.

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kjetil-lye/statistical_systems_paper_experimentsOfficial100%
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Experiments for the systems paper

30Shell, PythonMar 19, 20193 years agoMIT
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MIT

Experiments for the systems paper in 2d.

30Shell, PythonMar 7, 20197 years agoMIT

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Cite this paper

@article{fjordholm2019statistical,
  title  = {Statistical solutions of hyperbolic systems of conservation laws: numerical approximation},
  author = {Ulrik Skre Fjordholm and Kjetil Lye and Siddhartha Mishra and Franziska Weber},
  year   = {2019},
  eprint = {1906.02536},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1906.02536}
}

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