Metriplectic Integrators for the Landau Collision Operator
This work provides a general method for plasma physics simulations that guarantees physical conservation laws and entropy behavior for any finite element mesh, addressing a key challenge in numerical plasma modeling.
The authors developed a new framework for solving the nonlinear Landau collision integral using finite element methods that preserve the metriplectic structure, ensuring conservation of energy, momentum, particle densities, and entropy production in the fully discrete system.
We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonic behavior of entropy are guaranteed for finite element discretizations in general, independently of the mesh configuration.