Vlasov-Ampère方程的一种条件化表述：一种保持守恒性、正性、渐近性和高斯定律的格式
A conditional formulation of the Vlasov-Ampere Equations: A conservative, positivity, asymptotic, and Gauss law preserving scheme
AI总结：
提出Vlasov-Ampère方程的条件化变量重构，结合矩方程与慢流形约化，构建1D1V守恒、正性、高斯定律及准中性渐近保持数值格式。
摘要：
我们提出了一种针对等离子体Vlasov-Ampère方程的新型重构。该重构揭示了离散对称性，以实现质量、动量和能量的同时守恒；保持高斯定律对合性；分布函数的正性；以及准中性渐近性。我们的方法依赖于变量和坐标变换，从而得到一个由修正Vlasov方程及相关矩-场方程组成的耦合系统。修正Vlasov方程演化一个条件分布函数，该函数排除了关于质量、动量和能量密度的信息。质量、动量和能量密度则通过矩方程演化，其中强制执行离散对称性、守恒律和对合约束。该重构与最近的慢流形约化技术兼容，后者分离了快速电子时间尺度，并在更易求解的矩-场子系统内简化了对准中性渐近极限的处理。利用这一新表述，我们为约化的1D1V子系统开发了一种数值方法，该方法首次在保持准中性渐近极限的同时满足了重要的物理约束。我们通过典型的静电测试问题（包括多尺度离子声激波问题）展示了该方法的优势。
英文摘要：
We propose a novel reformulation of the Vlasov-Amp{è}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum, and energy; preservation of Gauss's law involution; positivity of the distribution function; and quasi-neutral asymptotics. Our approach relies on transforming variables and coordinates, leading to a coupled system of a modified Vlasov equation and the associated moment-field equations. The modified Vlasov equation evolves a conditional distribution function that excludes information on mass, momentum, and energy densities. The mass, momentum, and energy density, in turn, are evolved using moment equations, in which discrete symmetries, conservation laws, and involution constraints are enforced. The reformulation is compatible with a recent slow-manifold reduction technique, which separates the fast electron time scales and simplifies handling the asymptotic quasi-neutrality limit within the easier to solve moment-field subsystem. Using this new formulation, we develop a numerical approach for the reduced 1D1V subsystem that, for the first time, simultaneously satisfies the important physical constraints while preserving the quasi-neutrality asymptotic limit. The advantages of our approach are demonstrated through canonical electrostatic test problems, including the multiscale ion acoustic shock wave problem.
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