We present high-order accuracy simulations of the plasma-sheath transition with an ion–electron multi-fluid model that considers the electron inertial terms and the ion pressure gradient. By means of a third-order accuracy time-dependent finite volume scheme, we solve the isothermal multi-fluid equations with realistic ion-to-electron mass ratios. We propose a numerical procedure and boundary conditions that retrieve a steady-state solution of a planar 1D floating sheath. The classical solution to this problem neglects the ion temperature since the model equations present a singularity for a finite ion temperature. The multi-fluid simulations provide a rigorous solution to the plasma-sheath transition without singularities. We compare our solution to the classical theory, finding perfect agreement when the ion-to-electron temperature tends to zero. We discuss the effect of the ion temperature, the electron inertia, and the elastic collisions with neutrals in low-pressure plasmas...

中文翻译：

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低压条件下具有惯性项的多流体模型的等离子体-鞘层过渡：与经典理论和动力学理论的比较

我们用考虑了电子惯性项和离子压力梯度的离子-电子多流体模型对等离子体-鞘层过渡进行了高阶精度仿真。通过三阶精度随时间变化的有限体积方案，我们求解了具有实际离子电子质量比的等温多流体方程。我们提出了一个数值过程和边界条件，以检索平面一维浮鞘的稳态解。该问题的经典解决方案忽略了离子温度，因为模型方程式表示有限离子温度下的奇异性。多流体模拟为等离子体-鞘层过渡提供了严格的解决方案，而没有奇异之处。我们将我们的解决方案与经典理论进行了比较，当离子电子温度趋于零时找到了完美的一致性。