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.

# Applied Math Seminar: Numerical approximation of statistical solutions of hyperbolic systems of conservation laws given by Professor Franziska Weber (Carnegie Mellon University)

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