面向等离子体流体应用的广义曲线坐标新方法
Novel approach to general curvilinear coordinates for plasma fluid applications
- General Atomics（通用原子能）
- Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对一般几何中虚拟力导致的几何源项难题，提出一种重新表述的等离子体流体方程新方法，通过隐藏几何源项并保持离散守恒性质，在电阻磁流体系统中经液态金属流和Orszag-Tang涡验证正确性。
AI中文摘要：
在一般几何中，等离子体流体方程包含与虚拟力相关的非线性几何源项，这给计算机模拟带来了重大挑战。我们重新表述了等离子体流体层级，以严格保持对数值模拟至关重要的几何和守恒性质，同时隐藏几何源项。在离散形式下，重新表述的模型通过简单类比连续方程，自然地守恒质量、角动量和能量。这些守恒性质在离散空间中的要求极低，即一阶导数的反对称性以及标量积和叉积的正交性。通过解耦磁场几何、坐标系和数值离散化，这在保持物理保真度的同时实现了最大的灵活性。作为测试平台，我们将该新表述应用于电阻磁流体动力学系统，该系统涉及完整的曲线运算集合。我们使用稳态液态金属流动和经典的Orszag-Tang涡旋验证了该方法的正确性。
英文摘要：
In general geometry, plasma fluid equations include nonlinear geometric sources associated with fictitious forces, which pose significant challenges to computer simulations. We reformulate the plasma fluid hierarchy to rigorously preserve geometry and conservation properties critical to numerical simulations, while concealing the geometric sources. In their discrete form, the reformulated models conserve mass, angular momentum, and energy naturally, by simple analogy with the continuum equations. These conservation properties have minimal requirements in discrete space, namely, the anti-symmetry of the first derivative and the orthogonality of the scalar and cross products. By decoupling magnetic geometry, coordinate systems, and numerical discretization, this enables maximum flexibility while preserving physics fidelity. As a testbed, we apply the novel representation to the resistive magnetohydrodynamic system, which involves a complete set of curvilinear operations. We verify the correctness of the approach using steady state liquid metal flows and the classic Orszag-Tang vortex.
