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arXiv · 1906.02536

Statistical solutions of hyperbolic systems of conservation laws: numerical approximation

Ulrik Skre Fjordholm·Kjetil Lye·Siddhartha Mishra·Franziska Weber
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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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Ulrik Skre Fjordholm, Kjetil Lye, Siddhartha Mishra, Franziska Weber. 2019-06-06. Statistical solutions of hyperbolic systems of conservation laws: numerical approximation. https://arxiv.org/abs/1906.02536

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