Sharp interface immersed boundary method for simulating three-dimensional swimming fish

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 Karman street tends to appear when both the Strouhal number and tail-beating frequency are small, otherwise the double-row reverse Karman 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