This manuscript presents a benchmark problem for the simulation of single-phase flow,
reactive transport, and solid geometry evolution at the pore scale. The problem is organized …

This review paper presents an overview of Vortex Methods for flow simulation and their
different sub-approaches, from their creation to the present. Particle methods distinguish …

This paper is a study of incompressible fluids, especially their Clebsch variables and
vortices, using symplectic geometry and the Lie-Poisson structure on the dual of a Lie …

Recent contributions to vortex particle methods for the computation of three-dimensional
incompressible unsteady flows are presented. Both singular and regularized vortex particle …

The initial-value problem for perturbations of a flat, constant-strength vortex sheet is linearly
ill posed in the sense of Hadamard, owing to Kelvin-Helmholtz instability. Previous …

Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

A comprehensive review is presented of the computational methods based upon
Helmholtz's powerful concepts of vortex dynamics, making use of Lagrangian or mixed …

Singular terms in differential equations pose severe challenges for numerical
approximations on regular grids. Regularization of the singularities is a very useful …

Vortex methods of high order accuracy are developed for inviscid, incompressible fluid flow
in two or three space dimensions. The velocity kernels are smooth functions given by simple …

1. Weak and measure solutions of linear hyperbolic equations. 2. Generalities on the particle
method.•••..••• 3. Approximation of functions by Dirac measures.•.•• 4. Convergence of the …