Alexander Panchenko, anpanchenko@gmail.com
Non-local continuum models of particle systems
The main question addressed in the talk is how to obtain continuum equations for spatial averages from the
ODEs of classical particle dynamics. Balance equations for the average density, linear momentum, and energy
were derived by Irving and Kirkwood, Noll, Hardy, Murdoch and others. These equations are exact, but not in
closed form since fluxes are given as functions of particle positions and velocities. Evaluating the exact fluxes
requires solving the full ODE system which can be prohibitively expensive. We present a closure approximation
that leads to continuum models in the true sense of the word. The fluxes in these models are given by operators
acting on the average density and velocity. The closure construction is based on the use of regularized deconvolution. In the discrete setting, characterized by a finite non-improvable resolution, the error associated with
deconvolution closure can be further reduced by incorporating a priori knowledge of empirical statistics of fluctuations. At the end of the talk we briefly discuss connections with large eddy simulation and quasi-continuum
method. Results of numerical experiments and partial error estimates are presented as well