We present a novel numerical scheme for the efficient and accurate solution of the isothermal two-fluid (electron + ion) equations coupled to Poisson's equation for low-temperature plasmas at low-pressure. The model considers electrons and ions as separate fluids, comprising the electron inertia and space charge regions. The discretization of this system with standard explicit schemes is constrained by very restrictive time steps and cell sizes related to the resolution of the Debye length, electron plasma frequency, and electron sound waves. Both sheath and electron inertia are fundamental to fully explain the physics in low-pressure and low-temperature plasmas. However, most of the phenomena of interest for fluid models occur at speeds much slower than the electron thermal speed and are quasi-neutral, except in small charged regions. A numerical method that is able to simulate efficiently and accurately all these regimes is a challenge due to the multiscale character of the problem. In this work, we present a scheme based on the Lagrange-projection operator splitting that preserves the asymptotic regime where the plasma is quasi-neutral with massless electrons. As a result, the quasi-neutral regime is treated without the need of an implicit solver nor the resolution of the Debye length and electron plasma frequency. Additionally, the scheme proves to accurately represent the dynamics of the electrons both at low speeds and when the electron speed is comparable to the thermal speed. In addition, a well-balanced treatment of the ion source terms is proposed in order to tackle problems where the ion temperature is very low compared to the electron temperature. The scheme significantly improves the accuracy both in the quasi-neutral limit and in the presence of plasma sheaths when the Debye length is resolved. In order to assess the performance of the scheme in low-temperature plasmas conditions, we propose two specifically designed test-cases: a quasi-neutral two-stream periodic perturbation with analytical solution and a low-temperature discharge that includes sheaths. The numerical strategy, its accuracy, and computational efficiency are assessed on these two discriminating configurations.

我们提出了一种新颖的数值方案，用于高效，准确地求解等温双流体（电子+离子）方程，并与低压下低温等离子体的泊松方程耦合。该模型将电子和离子视为独立的流体，包括电子惯性和空间电荷区域。该系统采用标准显式方案的离散化受到非常严格的时间步长和与Debye长度，电子等离子体频率和电子声波分辨率相关的像元大小的限制。鞘层惯性和电子惯性都是充分解释低压和低温等离子体的物理学的基础。但是，流体模型感兴趣的大多数现象都以比电子热速度慢得多的速度发生，并且是准中性的，除了在较小的带电区域中。由于问题的多尺度特征，一种能够有效，准确地模拟所有这些状态的数值方法是一个挑战。在这项工作中，我们提出了一个基于拉格朗日投影算子分裂的方案，该方案保留了渐近状态，其中等离子体为准中性且无质量电子。结果，不需要隐式求解器，也不需要解析德拜长度和电子等离子体频率，就可以处理准中性状态。另外，该方案证明可以在低速和电子速度与热速度相当时准确地表示电子的动力学。另外，为了解决离子温度比电子温度低的问题，提出了离子源项的均衡处理。当解析德拜长度时，该方案显着提高了准中性极限和存在等离子鞘的精度。为了评估该方案在低温等离子体条件下的性能，我们提出了两个经过特殊设计的测试用例：带有分析溶液的准中性双流周期性扰动和包括鞘管的低温放电。数值策略，其准确性和计算效率在这两种区分配置上进行了评估。带有分析溶液的准中性双流周期性扰动和包括护套在内的低温放电。数值策略，其准确性和计算效率在这两种区分配置上进行了评估。带有分析溶液的准中性双流周期性扰动和包括护套在内的低温放电。数值策略，其准确性和计算效率在这两种区分配置上进行了评估。