保持守恒定律的柱坐标一维 MHD 流动不变有限差分格式
Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation
AI总结：
本文基于柱坐标一维磁流体力学方程的群分类，从经典完全守恒格式出发，构造了保持对称性与守恒定律的有限差分格式，并在有限和无限电导率下推导出多种新格式。
摘要：
基于近期对柱坐标几何中一维磁流体力学（MHD）方程的群分类，本文进行了保持对称性与守恒定律的有限差分格式的构造。新格式从经典的完全守恒 Samarsky-Popov 格式出发进行构造。在有限电导率情况下，推导出的格式容许所有对称性，并具备原始微分模型的所有守恒定律，包括此前未知的守恒定律。在磁场冻结（即电导率无限大）情况下，构造了多种具备守恒定律的格式，包括沿运动轨迹保持熵的格式。文中还讨论了针对特定形式的熵和磁通量，构造具有扩展守恒定律集格式的特点。
英文摘要：
On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky-Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
