An Assessment of Dual-Time Stepping, Time Spectral and Artificial Compressibility Based Numerical Algorithms for Unsteady Flow with Applications to Flapping Wings

The objective of this study is to compare and contrast three numerical algorithms that can be used to estimate the forces and pressure distribution on wings in flapping motion. All algorithms are used to solve the unsteady Navier-Stokes equations in two dimensions at low Reynolds Numbers. The four algorithms are a) an A-stable, implicit discretization b) the time-spectral algorithm that implicitly assumes that the flow-field in temporally periodic, c) incompressible formulations of a) and d) incompressible formulations of b) using the artificial com-pressibility method. The methods in a) and b) have been reported earlier in literature but their application to flapping wing flows at low Reynolds number is new. The algorithms introduced in c), and d) are new and previously not reported in literature. In this abstract, the four algorithms are used for roughly similar test cases to obtain preliminary estimates for their merits and demerits. The final version of the paper will use the same test case for all the algorithms to enable even-handed comparison of the different numerical methods. Background Insect flight control has been studied extensively from a physiological perspective, but its mechanics are not understood well. Even when the kinematic changes elicited by a given stimulus have been defined, their consequences for aerodynamic force production often remain obscure. Quasi-steady aerodynamics have been largely supplanted by unsteady theories and is widely accepted as the mechanism that leads to the forces produced by insects in flight. 3, 4 Lighthill 1 performed some of the earliest theoretical studies on the aerodynamics of insect flight shows the variation of lift and drag as observed by Weis-Fogh and Jensen. 2 A variety of experimental studies have enabled a better understanding of the nature of wing articulation by insects in hover and forward flight. While these studies enabled the authors to propose a variety of possible theories for insect flight, the lack of a complete understanding of the flight control mechanisms have prevented a more comprehensive understanding of insect flight control. It is not clear how many degrees of freedom an insect controls to enable it to perform its various maneuvers. Further, insects in controlled laboratory environments tend to produce lift and drag forces that are different from those observed in nature leading one to look for alternate analysis tools. It is also difficult to replicate subtle shifts in the center-gravity or even get a good estimate of the center of gravity …