Swimming Through Parameter Subspaces of a Simple Anguilliform Swimmer

Abstract

Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model parameters and performance is sensitive to those parameters. In this paper, parameter subspaces are qualitatively identified in which there exists enhanced swimming performance for an idealized, simple swimming model that resembles a C. elegan, an organism that exhibits an anguilliform mode of locomotion. The computational model uses the immersed boundary method to solve the fluid-interaction system. The 1D swimmer propagates itself forward by dynamically changing its preferred body curvature. Observations indicate that the swimmer’s performance appears more sensitive to fluid scale and stroke frequency, rather than variations in the velocity and acceleration of either its upstroke or downstroke as a whole. Pareto-like optimal fronts were also identified within the data for the cost of transport and swimming speed. While this methodology allows one to locate robust parameter subspaces for desired performance in a straight-forward manner, it comes at the cost of simulating orders of magnitude more simulations than traditional fluid-structure interaction studies.

Diving into a simple anguilliform swimmer's sensitivity

“…This paper explores the global sensitivity analysis of a mathematical model of a biological system -an idealized swimmer that resembles an aquatic nematode. The selection of an fluid-structure interaction model was two fold: (1) to illustrate that such global sensitivity analysis can be per-formed on a complex model and (2) to highlight the challenges (necessary computational resources) to perform such an analysis on a computational fluid dynamics model. The swimmer itself, in resembling a nematode, propagates itself forward through its fluid environment by varying its body curvature, i.e., bending [17,18,19,20], see Figure 1.…”

“…These organisms are much larger and live at intermediate Re (Re ∼ 10s or 100s) or higher Re (Re 1000) ranges. A recent computational study sought out to explore the effectiveness of this anguilliform gait across a variety of fluid scales, f , and intrinsic curvature dynamics [1]. This work is a continuation of the work in [1], which explored the same idealized, simple swimmer's anguilliform gait and swimming performance through thorough extensive parameter subspace explorations.…”

“…A recent computational study sought out to explore the effectiveness of this anguilliform gait across a variety of fluid scales, f , and intrinsic curvature dynamics [1]. This work is a continuation of the work in [1], which explored the same idealized, simple swimmer's anguilliform gait and swimming performance through thorough extensive parameter subspace explorations. The parameter space considered was composed a fluid scaling parameter, given by an input Reynolds number (Re in ), the stroke (undulation) frequency (f ), and a kinematic control parameter (p).…”

“…While [1] performed extensive parameter explorations using the same anguilliform swimmer model, specific 2D slices through the overall 3D parameter space were chosen in which to investigate swimming performance. The selected 2D slices were always perpendicular to other parameter in the 3D space.…”

“…The anguilliform swimmer model explored here has substantial forward swimming speeds when Re in 450 [1]. Therefore, with the goal of performing global sensitivity analyses, the parameter subspace selected to perform the analyses was Re ∈ [450, 2200], f ∈ [1, 3] Hz, and p ∈ [0.05, 0.45].…”