709 Modelling and Numerical Simulation of Non-Equilibrium Processes

James McDonald, University of Ottawa
Zhenning Cai, National University of Singapore
Hossein Gorji, RWTH University
Many classical physical models rely on an assumption of local thermodynamic equilibrium, such as the continuum hypothesis of the Euler and Navier-Stokes equations of fluid mechanics. However, for systems composed of many particles, a lack of particle interactions can often render this assumption unjustifiable. Kinetic models, such as the Boltzmann, Vlasov, Fokker-Planck and radiative-transport equations, retain validity in such situations, but at the expense of additional dimensions. Unfortunately, due to this high-dimensionality, the solution of full kinetic descriptions still remains largely intractable for many practical applications of interest, even when the power of advanced high-performance computing is brought to bear.

The kinetic equations governing a range of processes, for which non-equilibrium effects are expected, share a remarkably similar structure, including Hamiltonian mechanics/dynamics for particle motion in phase space and local integral operators describing particle interaction. Practical situations that are governed by such equations include rarefied gases, radiation transport, and multiphase flows. The similarity of the physics describing these situations means that modelling techniques and numerical methods that are appropriate for one situation is usually applicable across a wide range of physical processes. In particular, meso-scale models, which bridge the gap between the traditional continuum models and molecular based solution techniques, hold the promise of greatly expanding the range of physical regimes for which physically accurate solutions can be obtained at affordable numerical expense.

The purpose of this mini-symposium is to promote communication between researchers working on modelling and numerical solution in a wide field of related topics, such as rarefied gas dynamics, neutron transport and plasma physics. A range of techniques and methods are welcome, which include deterministic and stochastic numerical solvers, particle methods, moment methods, hybrid methods, and more.