TITLE:

PDF solutions of stochastic hyperbolic equations

DATE:

Friday, April 12th, 2013

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Daniel M. Tartakovsky.
Department of Mechanical and Aerospace Engineering.
University of California, San Diego.

ABSTRACT:

We develop a probabilistic approach to quantify parametric uncertainty in first-order hyperbolic conservation laws. The approach relies on the derivation of a deterministic equation for the cumulative distribution function (CDF) of system states, in which probabilistic descriptions (probability density functions or PDFs) of system parameters and/or initial and boundary conditions serve as inputs. In contrast to PDF equations, which are often used in other con- texts, CDF equations allow for straightforward and unambiguous determination of boundary conditions with respect to sample variables. We demonstrate the accuracy and robustness of our CDF approach in two settings: the Saint-Venant equations of river flows and the Buckley-Leverett equations of two-phase flow in porous media. In both cases, we obtain closed-form, semi-analytical solutions for the CDF of the state variables and test them against the results from Monte Carlo simulations.

HOST:

Dr. Gustaaf Jacobs.

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