Fast Triangulated Vortex Methods for the 2D Euler Equations

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 ...

Fast Adaptive 2D Vortex Methods

Fast Adaptive 2D Vortex Methods

On 2D Euler equations. I. On the energy–Casimir stabilities and the spectra for linearized 2D Euler equations

In this paper, we study a linearized two-dimensional Euler equation. This equation decouples into infinitely many invariant subsystems. Each invariant subsystem is shown to be a linear Hamiltonian system of infinite dimensions. Another important invariant besides the Hamiltonian for each invariant subsystem is found and is utilized to prove an ‘‘unstable disk theorem’’ through a simple energy–C...

Renormalized Solutions of the 2d Euler Equations

In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.