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

[摘要] In this thesis we present an accurate and efficient algorithm for computing idealflows using vortex sheets. A vortex sheet is a mathematical model simulating slightlyviscous flow in which the vorticity is concentrated on a surface and the viscous effectsare small. The sheet surface is represented by a set of triangular panels and eachpanel contains a set of active and passive Lagrangian particles. The active particlescarry vorticity and the passive particles are used for panel subdivision and particleinsertion. The method computes the vorticity carried by those particles, and thenthe 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 onlyuse information within each panel. The purpose of implementing the locality is toavoid taking derivatives of the flow map, which is difficult because the derivativesgrow in amplitude as time progresses. Computations of homogeneous flow, in whichvorticity is conserved, are presented. We also present results for slightly stratifiedflow, in which vorticity is generated baroclinically on the sheet.

[发布机构] University of Michigan

[效力级别] Sheet

[关键词] Vortex;Sheet;Adaptive;Triangular;Intrinsic;Mathematics;Science;Mathematics