The mesh deformation method is an important topic in studies involving moving boundary problems. As one of the main approaches, this method has been applied in various related studies. To address the cell inversion problem encountered in the spring analogy mesh deformation method, the present study proposes an improvement in it by cell-center concept. In addition to the linear spring between two nodal points on the mesh, the cell-center concept introduces additional fictitious springs between the cell-center and its nodal points. The spring constants for both actual and fictitious springs are modeled as reciprocals of the spring length. The final coordinates for each nodal point on the mesh are updated by assuming an equilibrium condition is achieved. For benchmark testing, the proposed method is compared with the original spring analogy and torsional spring analogy methods for rotating airfoil with inviscid mesh and multi-element airfoil with viscous mesh. It is observed that the cell-center spring analogy method alleviates the cell inversion problem that occurs in the original spring analogy method. Discussion concerning the performance of each method for the comparison is also included.

网格变形方法是涉及移动边界问题的研究中的重要课题。作为主要方法之一，该方法已在各种相关研究中得到应用。为了解决弹簧类比网格变形方法中遇到的单元倒置问题，本研究提出了一种基于单元中心概念的单元倒置改进方法。除了网格上两个节点之间的线性弹簧外，单元中心概念还在单元中心及其节点之间引入了其他虚拟弹簧。实际和虚拟弹簧的弹簧常数都被建模为弹簧长度的倒数。通过假设达到平衡条件，更新网格上每个节点的最终坐标。对于基准测试，将该方法与原先的弹簧类比法和扭转弹簧类比法进行了比较。可以看出，单元中心弹簧类比方法减轻了原始弹簧类比方法中发生的单元倒置问题。还包括有关每种比较方法的性能的讨论。