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：我们提出了一种高效的逐维有限体积方法，该方法采用受限输运方法在笛卡尔网格上以高阶离散格式求解绝热磁流体动力学方程。本文展示了直至十阶精度的计算结果。该方法每个计算单元每个面仅需一个重构值。通过高阶点值的过渡，计算成本随离散阶数增加而适度增长。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，在明显更粗的分辨率下即可实现可比较的精度结果，从而获得整体性能提升。此外，我们还提出了一种包含物理耗散项（粘性、磁扩散率和冷却函数）的方法，该方法同时满足有限体积和受限输运框架。