An Energy- and Charge-Conserving 5-moment Fluid Plasma Model
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Fluid plasma models are attractive due to their lack of statistical noise and low computational cost with respect to direct (``continuum") and particle-based (e.g., particle-in-cell) kinetic methods. Near equilibrium, 5-moment methods that solve the Euler equations coupled with electromagnetics are valid and cheap. For stronger non-equilibrium behavior, 5-moment methods are useful as a low-fidelity approximation either stand-alone or as part of a hybrid fluid-kinetic scheme, e.g., [1]. With this in mind, we note the development of robust, accurate, and structure-preserving numerical methods for fluid plasma models remains an active research challenge [2,3,4]. In this talk, we present an energy- and charge-conserving finite element scheme for a 5-moment fluid plasma model. In particular, we focus on energy conservation achieved through an operator splitting method inspired by the Boris push [5], the gold standard in time integration for particle-based kinetic methods. Standard Runge-Kutta schemes commonly employed to time advance the Euler equations can cause catastrophic failures (i.e., negative internal energy and pressure) if used naively with a fluid plasma model due to the energy exchange between the fluid and the electromagnetic fields. Our method allows for a physically-consistent exchange, and conservation of energy follows.
