Multi-resolution stochastic Galerkin methods for uncertain <br/><br/>hyperbolic flows

Monday, October 18, 2010 - 4:30pm - 5:30pm
Keller 3-180
Olivier Le Maître (Centre National de la Recherche Scientifique (CNRS))
We present a multi-resolution scheme, based on piecewise polynomial
approximations at the stochastic level, for the resolution of
nonlinear hyperbolic problems subjected to parametric
uncertainties. The numerical method rely on a Galerkin projection
technique at the stochastic level, with a finite-volume discretization
and a Roe solver (with entropy corrector) in space and time. A key
issue in uncertain hyperbolic problem is the loss of smoothness of the
solution with regard to the uncertain parameters, which calls for
piecewise continuous approximations and multi-resolution schemes,
together with adaptive strategies. However, discontinuities in the
spatial and stochastic domains are well localized, requiring very
different discretization efforts according to the local smoothness of
the solution. As a result, classical discretization approaches based
on the tensorization of stochastic and deterministic approximation
spaces (bases) are inefficient and we propose a numerical procedure
where the spatial discretization is fixed while the stochastic basis
is locally adapted in space to fit the solution complexity. Examples
of applications and efficiency / complexity assessment of the method
will be shown.
MSC Code: