Source-linked AI summary
An arbitrary Lagrangian-Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa \textit{Aequorea victoria}
Mehmet Sahin, Kamran Mohseni
TL;DR
The study examines flow around a free-swimming Aequorea victoria. It uses a geometrically conservative ALE formulation with fully coupled medusa motion and Navier–Stokes equations, reporting average swimming velocities on two meshes.
Problem
The study examines the flow pattern around a free-swimming Aequorea victoria.
Source: §1 · p. 2Method
A geometrically conservative ALE formulation is used, with the medusa’s equation of motion solved fully coupled with the Navier–Stokes equations.
Source: §1 · p. 2Results
1.453 cm/s on M1 and 1.462 cm/s on M2 are the computed average swimming velocities.
Source: §1 · p. 2Takeaways & Limitations
The reported average swimming velocities are close across the two meshes.
Source: §1 · p. 2
Abstract
from arXiv · showhide
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 \textit{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. The fluid dynamics video presented here shows the time variation of the instantaneous three-dimensional vorticity isosurfaces around a free-swimming hydromedusa \textit{Aequorea victoria}.
1 Introduction
The study applies a geometrically conservative ALE formulation to flow around a free-swimming Aequorea victoria, coupling medusa motion with the Navier–Stokes equations. It reports swimming velocities on two meshes and dimensionless flow parameters.
1 Introduction
- 1.453 cm/s on M1 and 1.462 cm/s on M2 are the computed average swimming velocities.The meshes contain 63,099 and 205,714 vertices, respectively.Source: §1 · p. 2
- The flow calculation uses a geometrically conservative ALE formulation and solves the medusa’s equation of motion fully coupled with the Navier–Stokes equations.The video shows time-varying instantaneous three-dimensional vorticity isosurfaces around the free-swimming medusa.Source: §1 · p. 2
- Based on M2 average velocity and maximum bell diameter, the Reynolds number is 672 and the Strouhal number is 8.47.Source: §1 · p. 2