Model order reduction for parametrized nonlinear hyperbolic problems as an application to Uncertainty Quantification

R. Crisovan, D. Torlo, R. Abgrall, S. Tokareva

Published 2018-08-09Version 1

In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are interested in model order reduction (MOR) techniques for unsteady non-linear hyperbolic systems of conservation laws, which involve moving waves and discontinuities, we explore the parameter-time framework and in the same time we deal with nonlinearities using a POD-EIM-Greedy algorithm \cite{Drohmann2012}. We provide under some hypothesis an error indicator, which is also an error upper bound for the difference between the high fidelity solution and the reduced one.