Related papers: A Characteristic Mapping Method for Vlasov-Poisson…

In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum…

We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth…

We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the…

In this work, we develop and rigorously analyze a new class of particle methods for the magnetized Vlasov--Poisson--Fokker--Planck system. The proposed approach addresses two fundamental challenges: (1) the curse of dimensionality, which we…

The velocity-space resolution required to accurately simulate kinetic phenomena in the 1D-1V Vlasov--Poisson system is generally not known a priori. In this work, we determine the upper bound on the resolution requirement for linear and…

We prove a local existence and uniqueness result for the non-relativistic and relativistic Vlasov-Poisson system for data which need not even be continuous. The corresponding solutions preserve all the standard conserved quantities and are…

A new computational method to solve the hyperbolic (Vlasov) equation and the elliptic (Poisson-like) equation at the polar axis is proposed. It is shown that the value of a scalar function at the polar axis can be predicted by its…

Presented in this paper is a new sparse linear solver methodology motivated by multigrid principles and based around general local transformations that diagonalize a matrix while maintaining its sparsity. These transformations are…

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…

We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove the uniqueness and the quantitative stability of Lagrangian…

In this work we propose a Hybrid method with Deviational Particles (HDP) for a plasma modeled by the inhomogeneous Vlasov-Poisson-Landau system. We split the distribution into a Maxwellian part evolved by a grid based fluid solver and a…

In this work, we use a moving Voronoi and sharp interface approach for simulating two-phase flows. At every time step, the mesh is generated anew from Voronoi seeds that behave as material points. The paper is a continuation of our previous…

In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is…

Following Fr\'enod and Sonnendr\"ucker, we consider the finite Larmor radius regime for a plasma submitted to a large magnetic field and take into account both the quasineutrality and the local thermodynamic equilibrium of the electrons. We…

We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…

The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO…

This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…

Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for…

We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…