A second order finite-difference numerical method is used to solve the Navier–Stokes equations of incompressible flow, in which the solid body with complex geometry is immersed into the fluid domain with orthogonal Cartesian meshes. To account for influences of the solid body, interactive forces are applied as boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the solid body. Fluid flow velocities in these nodes are reconstructed to track and control the deformation of the solid body, in which the local direction normal to the body surface is employed using the level-set function. The capabilities of this method are demonstrated by the application to fish swimming, and the computed behaviors of swimming fish agree well with experimental ones. The results elucidate that the ability of swimming fish to produce more thrust and high efficiency is closely related to the Reynolds number. The single reverse Kármán street tends to appear when both the Strouhal number and tail-beating frequency are small, otherwise the double-row reverse Kármán street appears. The algorithm can capture the geometry of a deformable solid body accurately, and performs well in simulating interactions between fluid flow and the deforming and moving body.

使用二阶有限差分数值方法来求解不可压缩流的Navier-Stokes方程，其中将具有复杂几何形状的实体浸入具有正交笛卡尔网格的流体域中。为了解决实体的影响，在位于外部但紧邻实体的笛卡尔网格节点处，将交互作用力作为边界条件施加。重建这些节点中的流体流速，以跟踪和控制固体的变形，其中使用水平集函数采用垂直于体表的局部方向。该方法在鱼类游泳中的应用证明了其功能，游泳鱼类的计算行为与实验结果吻合良好。结果表明，游泳鱼产生更大推力和高效率的能力与雷诺数密切相关。当Strouhal数和拍尾频率都较小时，倾向于出现单一的反向Kármán街道，否则会出现双向的反向Kármán街道。该算法可以准确地捕获可变形固体的几何形状，并且在模拟流体流与变形和运动体之间的相互作用方面表现出色。