Statistical analysis and simulation of random shock waves in Burgers turbulence
Professor Daniele Venturi
1pm, April 7th, 2014 (Monday)
Phillips Hall 736
Hosted by: Dr. Chunlei Liang (email@example.com)
In this talk I will present recent theoretical and numerical results on random shock waves in scalar conservation laws subject to random space-time perturbations and random initial conditions. By using the Mori-Zwanzig (MZ) formulation of irreversible statistical mechanics, I will derive exact reduced-order equations for the one-point and two-point probability density functions (PDF) of the solution field. In particular, I will consider the stochastic Burgers equation as a model problem and compute the statistical properties of random shock waves in the inviscid limit by using adaptive discontinuous Galerkin methods. Specifically, I will consider stochastic flows generated by high-dimensional random initial conditions and random additive forcing terms, yielding multiple interacting shock waves collapsing into clusters and settling down to a similarity state. I will also address the question of how random shock waves in space and time manifest themselves in probability space. The mathematical framework I will discuss is general and it can be applied to many disciplines, leading to new insights in high-dimensional stochastic dynamical systems and more efficient computational algorithms.
Daniele Venturi received the B.S. and Sc.M. degrees in Mechanical Engineering at the University of Bologna in 2002. Then he joined the Department of Energy, Nuclear and Environmental Engineering at the University of Bologna where he received the Ph.D. degree in thermo-fluid dynamics in 2006. Since 2010 he has been appointed as research assistant professor at the Division of Applied Mathematics at Brown University. His research interests embrace a wide range of topics. In particular, he has been working on theoretical and computational fluid dynamics, stochastic low-dimensional modeling and simulation of complex systems, probability density function methods and nonlinear functional analysis.