The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize unconditionally stable implicit time advance methods. Hybridizable discontinuous Galerkin (HDG) methods have emerged as a powerful tool for solving stiff partial differential equations. The HDG framework combines the advantages of the discontinuous Galerkin (DG) method, such as high-order accuracy and flexibility in handling mixed hyperbolic/parabolic PDEs with the advantage of classical continuous finite element methods for constructing small numerically stable global systems which can be solved implicitly. In this research we quantify the numerical stability conditions for the two-fluid equations and demonstrate how HDG can be used to avoid the strict stability requirements while maintaining high order accurate results.

翻译：双流体等离子体模型涵盖广泛的时标范围，无论等离子体动力学发生的时标如何，所有时标都必须进行数值解析。解决数值刚性系统的通用策略是采用无条件稳定的隐式时间推进方法。可混合不连续伽辽金（HDG）方法已成为求解刚性偏微分方程的有力工具。HDG框架兼具不连续伽辽金（DG）方法在应对混合双曲/抛物型偏微分方程时的高阶精度与灵活性优势，以及经典连续有限元方法构建可隐式求解的小规模数值稳定全局系统的优势。本研究定量分析了双流体方程的数值稳定性条件，并论证了HDG方法在规避严格稳定性要求的同时保持高阶精度求解结果的可行性。