Numerical simulation of the self-propulsive motion of a fishlike swimming foil using the δ+-SPH model

The present work is dedicated to the application of the recently developed (δ+-SPH) scheme to the self-propulsive fishlike swimming hydrodynamics. In the numerical method, a particle shifting technique (PST) is implemented in the framework of δ+-SPH, combining with an adaptive particle refinement (APR) which is a numerical technique adopted to refine the particle resolution in the local region and de-refine particles outside that region. This comes into being the so-called δ+-SPH scheme which contributes to higher numerical accuracy and efficiency. In the fishlike swimming modeling, a NACA0012 profile is controlled to perform a wavy motion mimicking the fish swimming in water. Thanks to the mesh-free characteristic of SPH method, the NACA0012 profile can undergo a wavy motion with large amplitude and move forward freely, avoiding the problem of mesh distortion. A parallel staggered algorithm is adopted to perform the fluid-structure interaction between the foil and the surrounding fluid. Two different approaches are adopted for the fishlike swimming problem. In Approach 1, the foil is fixed and flaps in a free stream and in Approach 2, the wavy foil can move forward under the self-driving force. The numerical results clearly demonstrate the capability of the δ+-SPH scheme in modeling such kind of self-propulsive fishlike swimming problems.