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Center for Nonlinear Studies |
In dissipationless systems, Hamiltonian mechanics, culminating in a Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy functional to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this talk, we review the basic principles of metriplectic dynamics and discuss some prominent methods for discretization that would preserve the mathematical structure of the equations. Specifically, we focus on the Vlasov-Maxwell-Landau model and, especially, on the Landau collision operator. Explicitly, we provide a recipe for constructing a metriplectic discretization of the collision operator and the first metriplectic formulation of collisional full-f electrostatic gyrokinetics with energy and momentum conservation laws.
Host: William Taitano