2018-02-07
10:15 at HCI J 498

Mathematical analysis and numerical schemes for dissipative dynamics like models

Gabriel Stoltz

Ecole des Ponts and Inria, Paris, France

I will first provide an introduction to what I believe to be a thermodynamically sound coarse-grained dynamics for molecular systems: dissipative particle dynamics with energy conservation (DPDE). In this framework, one molecule is represented by a single particle with an added variable, the internal energy. Another dynamics of interest is smoothed dissipative particle dynamics (SDPD), which provides a particular discretization of the Navier-Stokes equations, augmented by stochastic fluctuations whose magnitude is inversely proportional to the mass of the particle. From a structural viewpoint, this dynamics is very similar to DPDE when reformulated using internal energies instead of entropies. I will first provide a derivation of this reformulation of SDPD. I will next propose dedicated numerical schemes to integrate DPDE and SDPD, taking into account stabilities issues (avoiding negative internal energies) and parallelizability. I will conclude by presenting some applications to nonequilibrium systems - namely shock waves in molecular fluids.