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.

翻译：基于最近对圆柱几何中一维磁流体动力学（MHD）方程组的群分类，本文开展了具有对称性保持和守恒律的有限差分格式的构建工作。从经典的完全守恒型萨马尔斯基-波波夫格式出发，我们构建了新型差分格式。在有限电导率情形下，推导出了既保持原始微分模型所有对称性又拥有其全部守恒律（包括先前未知的守恒律）的格式。在冻结磁场（电导率无穷大）情形下，构建了多种具有守恒律的格式，其中包括沿运动轨迹保持熵的格式。针对具体的熵和磁通量形式，讨论了构建具有扩展守恒律集合的格式的若干特性。