Simulation of fish swimming and manoeuvring by an SVD-GFD method on a hybrid meshfree-Cartesian grid

Abstract

In this paper we present the development of the Singular-Value Decomposition (SVD) based Generalized Finite Difference (GFD) method for the simulation of fluid–structure interaction (FSI) problems in a viscous fluid. The class of FSI problems is exemplified by the self-propulsion (swimming) and dynamic manoeuvring of deforming (undulating and flexing) bodies in a fluid medium. Computation is carried out on a hybrid grid comprising meshfree nodes around the undulating swimming body and Cartesian nodes in the background. The meshfree nodes are convected in tandem with the changing shape and motion of the swimming body. The resultant locomotion of the swimmer is governed by fully-coupled dynamic interaction between the deforming body and the fluid in accordance with Newton’s laws. Time integration of motion is carried out by a Crank–Nicolson based implicit iterative algorithm, which fully couples the changing position of the swimming body with the evolving flow field, for numerical stability. The numerical scheme is applied to the steady swimming/cruising and sharp turning manoeuvres of a two-dimensional carangiform fish. The Strouhal number approaches values for efficient steady swimming reported in Fish and Lauder (2006) and Triantafyllou and Triantafyllou (1993) [3,6] at high Reynolds number. An illustrative example shows the numerical carangiform swimmer executing a sharp turn through an angle of 70° from straight coasting within a space of about one body length. The results obtained are consistent with available literature. In steady swimming, the momentumless wake theoretically anticipated by Wu (2001) [57] is successfully reproduced here, as opposed to the inverse von Karman vortex street generally predicted by inviscid flow models. The momentumless wake, characterized by an aligned series of alternately-signed shed vortices, is symptomatic of a state of average equilibrium between drag acting on the body of the fish and thrust produced by its undulating tail fin. Guided swimming towards targets based on a simple feedback control scheme is also demonstrated.