Parallel fully coupled Schwarz preconditioners for saddle point problems.
Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations ⋆⋆⋆
A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by...
Path following methods for steady laminar Bingham flow in cylindrical pipes
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
Path following methods for steady laminar Bingham flow in cylindrical pipes
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
Peristaltic transport in a cylindrical tube through a porous medium.
Peristaltic transport of an Oldroyd-B fluid in a planar channel.
Prediction-correction Legendre spectral scheme for incompressible fluid flow
Prediction-correction legendre spectral scheme for incompressible fluid flow
The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is proposed, which is easy to be performed. The numerical solution possesses the accuracy of second-order in time and higher order in space. The numerical experiments show the high accuracy of this approach.
Probabilistic analysis of singularities for the 3-D Navier-Stokes equations
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
The classical result on singularities for the 3D Navier-Stokes equations says that the -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently non degenerate...
Probabilistic models of vortex filaments
A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between and are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.
Probability & incompressible Navier-Stokes equations: an overview of some recent developments.
Produits rapides matrice-vecteur en bases d'ondelettes : application à la résolution numérique d'équations aux dérivés partielles
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains
We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal...
Pulsatile flow of two-fluid nonlinear models for blood flow through catheterized arteries: a comparative study.