An explicit semi-Lagrangian, spectral method for solution of Lagrangian transport equations in Eulerian-Lagrangian formulations

Conservative semi-Lagrangian schemes for Vlasov equations

Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case...

Semi-Lagrangian Methods for Level Set Equations

Semi-Lagrangian Particle Methods for Hyperbolic Equations

Particle methods with remeshing of particles at each time-step can be seen as forward semi-lagrangian conservative methods for advection-dominated problems, and must be analyzed as such. In this article we investigate the links between these methods and finite-difference methods and present convergence results as well as techniques to control their oscillations. We emphasize the role of the siz...

An Eulerian-Lagrangian approach to the Navier-Stokes equations

We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

0 An Eulerian - Lagrangian Approach to the Navier - Stokes equations