We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. This method requires only one reconstructed value per face for each computational cell. A passage through high-order point values leads to a modest growth of computational cost with increasing discretization order. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks.

翻译：本文提出一种高效的逐维有限体积方法，该方法采用笛卡尔网格上的约束输运技术，以高离散阶数求解绝热磁流体动力学方程组。计算结果展示了高达十阶精度的性能。该方法每个计算单元仅需每个面重构一个数值。通过高阶点值传递，计算成本随离散阶数增加仅适度增长。在给定分辨率下，这些高阶格式比常用低阶方法具有显著更低的数值耗散。因此，可在更粗分辨率下获得相当精度的计算结果，从而实现整体性能提升。我们还提出了一种在有限体积与约束输运框架内纳入物理耗散项（黏性、磁扩散和冷却函数）的方法。