Vortex methods rely principally on a discretization of the continuous two-dimensional time dependent vorticity eld into a large number of vortex \blobs", whose position and strength determine the underlying velocity eld. In this paper, the convergence of the random vortex method (RVM) for a complex ow is studied in function of three discretization parameters. Two of these parameters are related...

Chorin's vortex blob method has been proposed as a way to extend vortex sheet motion past the singularity formation time, into the physically important roll-up regime. Basic questions are: 1. Does the vortex blob method converge to an infinite spiral as the smoothing parameter tends to zero? 2. Do vortex blob computations approximate real fluid motion? This paper will present and discuss three ...

This paper presents a numerical comparison of two regularizations of the Euler equations, namely, the vortex blob regularization and regularization by physical viscosity. The initial condition is a flat vortex sheet whose vorticity has been smoothed by convolution. The sheet rolls up into a vortex pair. We compute the frequency of oscillations in the core vorticity and scale it using results fo...

In this paper, numerical simulation for a two-dimensional viscous and incompressible flow past the elliptical airfoil is presented by Random Vortex Blob (RVB). RVB is a numerical technique to solve the incompressible, two-dimensional and unsteady Navier-Stocks equations by converting them to rotational non-primitive formulations. In this method, the velocity vector at a certain point can be cal...

This article reviews some recent simulations of vortex sheet roll-up using the vortex blob method. In planar and axisymmetric flow, the roll-up is initially smooth but irregular small-scale features develop later in time due to the onset of chaos. A numerically generated Poincaré section shows that the vortex sheet flow resembles a chaotic Hamiltonian system with resonance bands and a heterocli...

We prove the convergence of vortex blob methods to classical weak solutions for the twodimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size ...

Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regulariz...

The vortex-blob method is extended to compute vortex sheet separation at a sharp edge. A smoothing parameter con­ trols the amount of detail occuring in the rolled-up spiral. Cal­ culations are presented for the case of vortex sheet roll-up due to an impulsively started flat plate.

Abstract. Motivated by classical vortex blob methods for the Euler equations, we develop a numerical blob method for the aggregation equation. This provides a counterpoint to existing literature on particle methods. By regularizing the velocity field with a mollifier or “blob function”, the blob method has a faster rate of convergence and allows a wider range of admissible kernels. In fact, we ...

We develop a boundary integral method for computing the motion of an interface separating two incompressible, inviscid fluids. The velocity integral is regularized, so that the vortex sheet on the interface is replaced by a sum of ‘‘blobs’’ of vorticity. The regularization allows control of physical instabilities. We design a class of high order blob methods and analyze the errors. Numerical te...