Abstract:  Random noise can dramatically change the response of a nonlinear dynamical system near critical and fully developed states as evidenced, for instance, by experimental results on the effects of free-stream turbulence in flows past spheres and thermal boundary layers. To model such noisy nonlinear dynamical systems and to understand the interaction between extrinsic and intrinsic stochasticity, we have developed new approaches that can extend current direct numerical simulation capabilities. These approaches address major challenges in the simulation of random systems such as high dimensions, discontinuities in probability space and random frequencies. In this talk we will present a multi-pronged approach to reduced order stochastic modeling that includes polynomial chaos, probabilistic collocation, nonlinear biorthogonal techniques and probability density function methods. We will illustrate the main ideas and their effectiveness with reference to prototype stochastic flow problems.

Bio:  Dr. Venturi earned his Ph.D. from the University of Bologna in 2006, and since that time has been at Brown University, first as a post-doctoral scholar and currently as a Visiting Assistant Professor. Dr. Venturi’s research focus is on fluid mechanics, with an emphasis on stochastic behaviors.