Structure-preserving finite element approximations of a hybrid relativistic cold fluid-particle model

2025/10/13 by Mukhamet, Tileuzhan, Kormann, Katharina
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2510.11500

Abstract

We derive mixed finite element discretizations of a cold relativistics fluid model from approximations of the Poisson bracket that preserve mass, energy and the divergence constraints. For time-discretization we derive an implicit energy-conserving average-vector field method or apply an explicit strong-stability preserving Runge-Kutta scheme. We also consider a coupling of the fluid model to relativistic particles. We perform a numerical study of the scheme which shows convergence and conservation properties of the proposed methods and apply the new scheme to a plasma wake field simulation.

Citations

• Time-splitting methods for the cold-plasma model using Finite Element Exterior Calculus
• A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and div B = 0
• A Variational Finite Element Discretization of Compressible Flow
• GEMPIC: geometric electromagnetic particle-in-cell methods
• On Hyperbolicity of 13-Moment System
• Viscous regularization of the Euler equations and entropy principles

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