Fish-like swimming is fascinating not only for its fundamental scientific value but also for engineering biomimetically inspired vehicles. Discovering physical principles behind the evolution of different aquatic swimmers can drastically improve the design of such vehicles. We are interested in the evolution of different caudal fin profiles (shape) because it is hypothesized that most of the thrust force is generated by the caudal fin. In fact, the caudal fin shape varies from hemocercal in mackerel to almost trapezoidal in trout and heterocercal in sharks. We investigate if such shape differences have hydrodynamic implications using numerical simulations.
The equations governing the fluid motion are solved in the non-inertial reference frame attached to the fish center of mass (COM) via the curvilinear/immersed boundary method (CURVIB), which is capable of carrying out direct numerical simulation of flows with complex moving boundaries. The motion of the fish body is prescribed based on carangiform kinematics while the motion of the COM is calculated based on the fluid forces on the fish body through the fluid-structure interaction algorithm of Borazjani et. al. (2008) [3]. The reader is referred to Borazjani & Sotiropoulos (2010) [4] for the details of the method.
For self-propelled simulations, the virtual swimmers start to undulate in an initially stagnant fluid and the swimming speed is determined based on the forces on the fish body. Therefore, physical parameters based on the swimming velocity change as the swimmer accelerates until the quasi-steady state is reached. The computational domain and time step for the self-propelled fish body simulations in the free stream is a cuboid with dimensions 2LxLx7L, which is discretized with 5.5 million grid nodes. The domain width 2L and height L are more than ten times the mackerel width 0.2L and height 0.1L, respectively. The fish is placed 1.5L from the inlet plane in the axial direction and centered in the transverse and the vertical directions. The simulations are partly run on our in-house computing cluster, Nami, with a total of 448 computing cores distributed across 28 nodes, each node containing a 2x8 Magny-Cours core (AMD 2.0 GHz). The memory available is 2GB RAM/core, 896GB total and the nodes are connected through QDR Infiniband. Some of the simulations were run on the dual-quad core nodes in the u2 cluster at CCR; these are also connected through QDR Infiniband.
The simulations generate velocity field data in VTK format [5], allowing one to apply ParaView's tetrahedralize algorithm [2] to the 5.5 million point data set. The result is shown in Figure 1 for a swimming mackerel, where volume rendered points are colored by the magnitude of the velocity field. The domain has been truncated in the vicinity of the fish and an appropriate colormap has been chosen to emphasis dynamics local to the fish. For each time-step and viewing angle, the tetrahedralize algorithm is applied. A single frame takes (at least) 10 minutes to render on an Intel dual-quad core node (w/ 24GB RAM). An animation of 95 frames was generated in a batch job using off-screen rendering. The animation can be downloaded at [1].