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Numerical approximation of statistical solutions of hyperbolic systems of conservation laws

Analysis, Dynamics, and Applications Seminar

Numerical approximation of statistical solutions of hyperbolic systems of conservation laws
Series: Analysis, Dynamics, and Applications Seminar
Location: Online
Presenter: Franziska Weber, Department of Mathematical Sciences, Carnegie Mellon University

Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions for multi-dimensional hyperbolic systems of conservation laws. We present a numerical algorithm to approximate statistical solutions of conservation laws and show that under the assumption of ‘weak statistical scaling’, which is inspired by Kolmogorov’s 1941 turbulence theory, the approximations converge in an appropriate topology to statistical solutions. We will show numerical experiments which indicate that the assumption might hold true.

Zoom: https://arizona.zoom.us/j/99410014231
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