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Computational challenges in the stochastic modeling of fluid mechanics

Daniele Venturi
Brown University


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.

Friday, November 16, 2012
11:00AM AP&M 6402