Applied Math Seminar: Numerical approximation of statistical solutions of hyperbolic systems of conservation laws given by Professor Franziska Weber (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.