We report on developments of a second-order, conservative, sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods operating on unstructured meshes. The remapping uses concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA).The non-oscillatory infinite gauge option of MPDATA remapping is derived in volume coordinates and is based upon a general and compact edge-based data structure, developed for use within an arbitrary finite volume framework. A Flux Corrected Transport style of limiting ensures monotonicity preservation, while the construction of volume coordinates utilises median dual polygonal finite volume cells.Theoretical developments are supported by numerical testing involving idealised cases with prescribed mesh movement for advection of scalars. The numerical investigations include an asymptotic mesh convergence study and comparisons with both MPDATA and Van Leer MUSCL remapping schemes operating on Cartesian meshes. The results demonstrate that the proposed scheme is suitable for providing accurate ALE remapping for unstructured meshes.

中文翻译：

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非结构化网格的多维正定重映射算法

我们报告了在非结构化网格上运行的任意拉格朗日-欧拉 (ALE) 方法的二阶、保守、符号保留重映射方案的发展。重新映射使用多维正定对流传输算法 (MPDATA) 的概念。 MPDATA 重新映射的非振荡无限规范选项是从体积坐标中导出的，基于通用且紧凑的基于边缘的数据结构，开发用于在任意有限体积框架。通量校正传输限制风格确保单调性保持，而体积坐标的构造利用中值双多边形有限体积单元。理论发展得到数值测试的支持，这些数值测试涉及具有指定网格运动的理想化案例，用于标量平流。数值研究包括渐近网格收敛研究以及与 MPDATA 和 Van Leer MUSCL 重映射方案在笛卡尔网格上运行的比较。结果表明，所提出的方案适用于为非结构化网格提供准确的 ALE 重映射。