Applying Conservation of Finite Volume Adaptive Methods to the Atmospheric Dynamic Framework

Existing r-adaptive moving mesh methods in atmospheric dynamics are predominantly based on finite element methods. They suffer from inherent conservation degradation and are highly sensitive to mesh distortion, making it difficult to meet the stringent requirements for long-term mass and energy conservation in atmospheric simulations. Furthermore, applying r-adaptive methods to three-dimensional (3D) structured hexahedral meshes faces significant challenges, including non-coplanar geometries and the loss of conservation during physical variable reconstruction. To address these issues, this paper proposes a conservative r-adaptive moving mesh method based on a finite volume scheme, specifically designed for atmospheric dynamical cores. By introducing a moving mesh equation to prevent mesh tangling, and employing a hexahedral element decomposition and block-integration reconstruction strategy, the method strictly guarantees mass and energy conservation even under severe geometric deformation. Validated through two-dimensional (2D) and 3D rising thermal bubble and flow-over-mountain test cases, the results demonstrate that the proposed method significantly enhances the resolution of strong-gradient, small-scale regions using fewer total grid points. It also maintains robust mass and energy conservation while achieving favorable parallel efficiency and scalability. This study provides a novel and efficient numerical solution for multi-scale atmospheric dynamical simulations.