Related papers: An Adaptive, Implicit, Conservative 1D-2V Multi-Sp…
We consider the solution of the fully kinetic (including electrons) Vlasov-Amp\`ere system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian…
We develop a conservative phase-space grid-adaptivity strategy for the Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is normalized to the thermal speed and shifted by the bulk-fluid velocity. The…
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
We propose a spectral method for the 1D-1V Vlasov-Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling $\alpha$ and shifting $u$ of the velocity…
The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the…
We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with the Poisson equation, which is a {classical mean-field} primary model for collisional plasmas. Two subproblems, i.e. the…
We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an…
We propose an explicit particle method for the Vlasov-Fokker-Planck equation that conserves energy at the fully discrete level. The method features two key components: a deterministic and conservative particle discretization for the…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the…
In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\mathbb T^d…
We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution of particles (e.g.$\,\,$in a plasma) undergoing diffusion,…
We develop and analyze a class of structure-preserving discontinuous Galerkin schemes for the nonlinear Vlasov-Poisson-Fokker-Planck model, reformulated as a hyperbolic system through a Hermite expansion in the velocity variable. We…
A conservative discrete velocity method (DVM) is developed for the ellipsoidal Fokker-Planck (ES-FP) equation in prediction of non-equilibrium neutral gas flows in this paper. The ES-FP collision operator is solved in discrete velocity…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
Fusion plasma and space plasma are typical non-equilibrium and nonlinear systems, with the interactions between different species well described by the Vlasov-Fokker-Planck (VFP) equations. The transport of mass, momentum, energy, and…
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence…
We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov- Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov…
A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the…