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.

翻译：我们通过保持质量、能量及散度约束的泊松括号近似，推导了冷相对论流体模型的混合有限元离散格式。在时间离散方面，我们推导了隐式能量守恒平均向量场方法，或采用显式强稳定保持Runge-Kutta格式。我们还考虑了流体模型与相对论粒子的耦合。通过数值研究验证了所提方法的收敛性与守恒特性，并将新格式应用于等离子体尾波场模拟。