Simulation of flow patterns generated by the hydromedusa Aequorea victoria using an arbitrary Lagrangian–Eulerian formulation

MOHSENI, Kamran

Simulation of flow patterns generated by the hydromedusa Aequorea victoria using an arbitrary Lagrangian–Eulerian formulation

Abstract

A new geometrically conservative arbitrary Lagrangian–Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian–Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier–Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc library. The present ALE method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free-swimming hydromedusa Aequorea victoria (crystal jellyfish). The calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa. In addition, the propulsion efficiency of the free-swimming hydromedusa is computed and its value is compared with values from the literature for several other species.

Description

The animation show the three-dimensional vorticity field around a free-swimming hydromedusa Aequorea victoria (crystal jellyfish).

Sponsorship

This work was partially supported by the National Science Foundation and the Air Force Office of Scientific Research.

Date Issued

2009-03-31

Publisher

Science Direct

Keywords

ALE methods; Jellyfish swimming; Geometric Conservation Law (GCL)

Previously Published As

Journal of Computational Physics 228 (2009) 4588–4605 --- The Journal of Experimental Biology 212, 2656-2667

ISSN

doi:10.1016/j.jcp.2009.03.027
doi:10.1242/jeb.025536

Types

article