Computational challenges in the stochastic modeling of fluid mechanics
Daniele Venturi
Brown University
Abstract:
Random noise can dramatically change the response of a fluid system near
critical and fully developed states as evidenced, for instance, by
experimental results on the effects of free-stream turbulence on
temperature boundary layers and on the drag crisis in flows past spheres.
To model such noisy nonlinear dynamical systems and to understand the
interaction between extrinsic and intrinsic stochasticity, many different
approaches have been recently proposed. However, even with recent
theoretical and computational advancements, no broadly applicable technique
has yet been developed for dealing with the challenging problems of high
dimensionality, possible discontinuities in probability space and
random frequencies. In this talk we will present a multi-pronged approach
to stochastic fluid mechanics that includes polynomial chaos, probabilistic
collocation, Wick-Malliavin approximations and probability density function
methods. We will illustrate the main ideas and their effectiveness with
reference to prototype stochastic flow problems.