Investigation of Two-Dimensional Incompressible Inviscid Axisymmetric Elliptical Vortices Using a Vortex-In-Cell Method

• Main Author: Chaudhary, Munwwar Mansoor
• Other Authors: Milane, Roger
• Language: en
• Published: Université d'Ottawa / University of Ottawa 2014
• Online Access: http://hdl.handle.net/10393/31192; http://dx.doi.org/10.20381/ruor-3788

A Vortex-In-Cell (VIC) scheme is implemented to study the evolution of two-dimensional elliptical vortices in a periodic domain. The mixed Eulerian-Lagrangian vortex-in-cell method adopted in this study is chosen because of its low dissipation errors and low computational cost. The goal of this thesis is to implemented this vortex-in-cell method and study how incompressible, inviscid elliptical vortices evolve. It is found that, through a process of filamentation, an initial vorticity profile evolves to a final axisymmetric configuration. It is found that the rate of axisymmetrization is controlled by the initial aspect ratio of the vortex. This thesis provides a practical overview of the numerical solution of inviscid, incompressible two-dimensional flows using the vortex-in-cell method. The computational domain is enclosed by an Eulerian mesh and the vorticity field is discretized into a finite set of Lagrangian elements (vortex particles). A Poisson equation is solved on the mesh at each time instance to compute the velocity field. The interpolation scheme is used to exchange vorticity and velocity information between the Lagrangian particles and the Eulerian grid. Vortex-particle locations are integrated in time using a predictor-corrector time integration scheme. Highly resolved solutions using a pseudo-spectral method are used as a benchmark to verify the vortex-in-cell implementation and to study solution convergence as a function of each parameter of the scheme. In addition, the vortex-in-cell method is validated by comparing with other related numerical studies. Finally, the evolutions of several initially elliptical vortex distributions with different aspect ratios are studied.