Fast Adaptive 2D Vortex Methods

Fast Adaptive 2D Vortex Methods

Fast Adaptive 2D Vortex Methods

Fast Vortex Methods

We present three fast adaptive vortex methods for the 2D Eu-ler equations. All obtain long-time accuracy at almost optimal cost by using four tools: adaptive quadrature, free-Lagrangian formulation, the fast multipole method and a nonstandard error analysis. Our error analysis halves the diierentiability required of the ow, suggests an eecient new balance of smoothing parameters , and combines ...

A Fast Adaptive Vortex Method in Three Dimensions *

The method of local corrections (MLC) developed by Anderson for two spatial dimensions is a particle-particle panicle-mesh method. in which the calculation of the velocity field induced by a collection of vortices is split into two parts: (i) a finite difference velocity field calculation using a fast Poisson solver, the results of which are used to represent the velocity field induced by vorti...

Fast Triangulated Vortex Methods for the 2-d Euler Equations

Vortex methods for inviscid incompressible two-dimensional uid ow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An e cient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the ...