Progress and Prospects of Cartesian Mesh Simulation Methods for Compressible Flow Problems

The computational grid is an essential prerequisite for the accurate simulation of complex flow problems, significantly influencing the accuracy and reliability of the numerical results. However, generating high-quality computational meshes requires a time-consuming and laborious human-machine interaction process that heavily depends on the personal expertise of engineers, resulting in a relatively low level of automation in computational fluid dynamics (CFD) at this stage. Cartesian grids have the characteristics of simple generation, low memory requirements, high computational efficiency, and strong automation, which can substantially reduce labor costs during mesh generation. Consequently, they have emerged as a prominent research focus within the CFD community. This paper primarily examines Cartesian grid method for the compressible flow simulations, integrating years of research findings from our group and reviewing key technologies alongside domestic and international development trends. Firstly, this paper briefly summarizes the adaptive methods and data structures of Cartesian meshes. Subsequently, it systematically describes the development status and existing challenges of techniques such as cut-cell, immersed boundary, overlapping Cartesian mesh, and hybrid Cartesian mesh methods. Finally, this paper discusses critical technologies and future development trends of Cartesian grid methods from various perspectives, including adaptive refinement strategies, dynamic parallel technology, high-fidelity computing methods, advanced physical models, and practical engineering applications. Through comprehensive reviews and in-depth analyses of the current research status and development of the Cartesian grid methods, this paper aims to provide readers with a clear and comprehensive understanding, and offer valuable references and insights for related field research.