四边形网格上CESE格式的自适应网格细化算法
Adaptive mesh refinement algorithm for CESE schemes on quadrilateral meshes
AI总结：
本研究提出时空CESE方法在自适应非结构四边形网格上的构造，设计基于cell-tree-vertex数据结构的新算法管理网格自适应，并集成多种CESE格式，通过可压缩无粘流模拟验证了其有效性。
摘要：
本研究提出了时空守恒元与解元（CESE）方法的构造，以适应自适应非结构四边形网格。随后，设计了一种新算法来有效管理交错格式的网格自适应过程，利用独特的cell-tree-vertex数据结构加速守恒元的构造并简化计算单元间的互连。展示了二阶a-α、Courant数不敏感和迎风CESE格式与该自适应算法的集成。开展了针对可压缩无粘流的数值模拟，以验证扩展格式和自适应算法的有效性。
英文摘要：
This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the mesh adaptation process for staggered schemes, leveraging a unique cell-tree-vertex data structure that expedites the construction of conservation elements and simplifies the interconnection among computational cells. The integration of second-order a-α, Courant number-insensitive, and upwind CESE schemes with this adaptation algorithm is demonstrated. Numerical simulations focusing on compressible inviscid flows are carried out to validate the effectiveness of the extended schemes and the adaptation algorithm.
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