Vortex Sheet Simulations of 3D Flows Using an Adaptive Triangular Panel/Particle Method.

Abstract

In this thesis we present an accurate and efficient algorithm for computing ideal flows using vortex sheets. A vortex sheet is a mathematical model simulating slightly viscous flow in which the vorticity is concentrated on a surface and the viscous effects are small. The sheet surface is represented by a set of triangular panels and each panel contains a set of active and passive Lagrangian particles. The active particles carry vorticity and the passive particles are used for panel subdivision and particle insertion. The method computes the vorticity carried by those particles, and then the induced velocities are computed with a tree-code. As the sheet surface evolves, stretching and twisting occur, hence refinement is needed to maintain resolution. The quadrature and the refinement procedure are local in the sense that they only use information within each panel. The purpose of implementing the locality is to avoid taking derivatives of the flow map, which is difficult because the derivatives grow in amplitude as time progresses. Computations of homogeneous flow, in which vorticity is conserved, are presented. We also present results for slightly stratified flow, in which vorticity is generated baroclinically on the sheet.