A data transfer (remap) between two meshes is an important step of each arbitrary Lagrangian-Eulerian (ALE) simulation. We develop a conservative scheme for remapping high-order discontinuous Galerkin fields on high-order polytopal meshes with curved faces. This scheme uses a virtual element function to define the remap velocity. We show that the optimal accuracy is achieved when the remap problem is written and is solved as a coupled system of two conservative equations. The properties of the proposed scheme are studied numerically for smooth and discontinuous fields on cubic and prismatic meshes.

中文翻译：

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曲线多面体网格上的保守高阶不连续Galerkin重映射方案

两个任意网格之间的数据传输（重映射）是每个任意拉格朗日-欧拉（ALE）模拟的重要步骤。我们开发了一种保守方案，用于在曲面高阶多面网格上重新映射高阶不连续Galerkin场。该方案使用虚拟元素函数定义重映射速度。我们表明，当编写重映射问题并将其作为两个保守方程的耦合系统进行求解时，可以实现最佳精度。对立方和棱柱形网格上的平滑场和不连续场进行了数值研究。