保持二阶散度约束的熵稳定有限差分格式用于理想双流体等离子体流动方程
Second order divergence constraint preserving entropy stable finite difference schemes for ideal two-fluid plasma flow equations
AI总结：
针对忽略黏性、电阻和碰撞效应的理想双流体等离子体流动方程，提出了一种二阶精度、熵稳定且保持散度约束的同位有限差分格式，通过多维Riemann求解器和IMEX时间离散确保电磁场散度约束的一致演化。
摘要：
双流体等离子体流动方程描述了具有不同密度、速度和压力的离子与电子的流动。我们考虑理想等离子体流动，即忽略黏性、电阻和碰撞效应。所得方程组的通量由三个独立分量组成：一个对应离子，一个对应电子，以及一个用于电磁场的线性 Maxwell 方程通量。这些分量通过源项进行耦合。在本文中，我们提出了守恒型二阶有限差分格式，以确保电场和磁场的散度约束的一致演化。核心思想是利用顶点处的多维 Riemann 求解器为 Maxwell 方程设计数值求解器，从而确保离散散度约束；对于流体部分，我们采用熵稳定离散方法。所提出的格式是同位的、二阶精度的、熵稳定的，并确保磁场的无散度演化。我们采用显式和隐式-显式（IMEX）格式进行时间离散。为了验证所提格式的精度、稳定性和散度约束保持能力，我们在一维和二维情况下展示了多个测试算例。我们还将数值结果与无散度清理的格式以及采用基于完美双曲 Maxwell（PHM）方程散度清理方法的 Maxwell 方程求解结果进行了比较。
英文摘要：
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of equations has flux consisting of three independent components, one for ions, one for electrons, and a linear Maxwell's equation flux for the electromagnetic fields. The coupling of these components is via source terms. In this article, we present {conservative} second-order finite difference schemes that ensure the consistent evolution of the divergence constraints on the electric and magnetic fields. The key idea is to design a numerical solver for Maxwell's equations using the multidimensional Riemann solver at the vertices, ensuring discrete divergence constraints; for the fluid parts, we use an entropy-stable discretization. The proposed schemes are co-located, second-order accurate, entropy stable, and ensure divergence-free evolution of the magnetic field. We use explicit and IMplicit-EXplicit (IMEX) schemes for time discretizations. To demonstrate the accuracy, stability, and divergence constraint-preserving ability of the proposed schemes, we present several test cases in one and two dimensions. We also compare the numerical results with those obtained from schemes with no divergence cleaning and those employing perfectly hyperbolic Maxwell (PHM) equations-based divergence cleaning methods for Maxwell's equations.
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