# A Novel Cell-Based Adaptive Cartesian Grid Approach for Complex Flow Simulations
## 1 Introduction  
With the widespread application of computational fluid dynamics (CFD) in fields such as rail transport and aerospace engineering, the complexity of geometric shapes that need to be processed has significantly increased [1]. For instance, the addition of pantographs and bogies to high-speed trains is required to assess the flow field around the entire train, which consequently places higher demands on mesh generation technologies [2; 3]. Particularly, the distribution of mesh density often depends on the prior estimation of flow characteristics [4], meaning that even seasoned mesh generation engineers may require weeks, if not longer, to create a high-quality mesh for complex geometries. Given the diversity of flow states in engineering problems, customizing mesh configurations for each specific flow state requires a tremendous amount of work [5]. Therefore, NASA has pointed out in its \"CFD Vision 2030\" that mesh generation and adaptivity continue to represent critical bottlenecks in the CFD workflow [6]. Research into adaptive mesh refinement (AMR) technology can be traced back to the 1980s [7], with capabilities for initial mesh densification based on geometrical shapes before computation, and dynamic refinement during the solution of governing equations based on flow characteristics [8; 9]. The quadtree/octree data structure of Cartesian grids naturally fits with AMR, and [PERSON] [10] was among the first to introduce AMR based on the quadtree/octree structure into Cartesian grids. Furthermore, the favorable orthogonality of the grid facilitates the computation of flow field gradients, making it easier to capture flow features. In summary, AMR technology has been a significant driving force behindthe further development of Cartesian grids, leading some scholars to believe that adaptive Cartesian grids may herald the third major breakthrough in CFD [1]. The AMR approaches under the Cartesian grid framework can be categorized into two types: block-based AMR [11] and cell-based AMR [12; 13]. Block-based AMR further divides into patch-based and block-structured adaptations [14]. The patch-based method creates regular, arbitrarily oriented rectangular patches, which are superimposed over areas with insufficient grid resolution to enhance the local resolution, first introduced by [PERSON] and [PERSON] [15]. In this approach, the grid hierarchy consists of nested, overlapping grids of increasingly higher resolution and does not require a tree data structure to describe the connectivity between blocks. Notable software libraries utilizing patch-based AMR methods include Chombo [16], Samrai [17], and Enzo [18], demonstrating solid performance across various simulation domains. Block-structured AMR, initially proposed and developed by [PERSON] [19] and [PERSON] [20] among others, can be seen as a simplified variant of the patch-based adaptation. Its characteristic feature is that the entire computational domain is divided into multiple non-overlapping blocks with an identical number of grid cells; the subject of refinement is the block itself, with adaptive history information maintained in a quadtree/octree data structure [21]. Global block refinement may lead to local grid over-densification and consequent memory waste. For example, given an enrichment threshold of 0.7 [22], a block would be refined if more than 70% of its cells were marked for refinement, rendering the remaining 30% as inefficiently refined. This raises another issue, namely the efficiency of block partitioning, requiring further research on how to divide the domain to ensure the most effective use of the refinement threshold. Evidently, both patch-based and block-structured adaptations lack overall flexibility and can be resource-intensive [23]. In contrast, the cell-based AMR introduced by [PERSON] et al. [24] also utilizes quadtree/ octree data structures for storage, selectively refining individual cells during the adaptive process.