Related papers: Energy-conserving discontinuous Galerkin methods f…
In this paper, we generalize the idea in our previous work for the Vlasov-Amp\`{e}re (VA) system \cite{cheng_va} and develop energy-conserving discontinuous Galerkin (DG) methods for the Vlasov-Maxwell (VM) system. The VM system is a…
In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov-Amp\`{e}re (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The algorithm is generalized from our previous work…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
We present a computational study for a family of discontinuous Galerkin methods for the one dimensional Vlasov-Poisson system that has been recently introduced. We introduce a slight modification of the methods to allow for feasible…
In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin(ECSLDG) method for the Vlasov-Ampere system. The method employs a semi-Lagrangian discontinuous Galerkin scheme for spatial discretization of…
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate…
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 present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard…
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…
In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian evolution equations. These systems often arise…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg-de Vries equation. We demonstrate that the scheme conserves energy up to machine precision. In this sense the method is consistent with the…
We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple…
This paper presents high-order Runge-Kutta (RK) discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry. The scheme can preserve a general polytropic equilibrium state and achieve total energy conservation up to…
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly…
We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen-Cahn/Cahn-Hilliard/Navier-Stokes-Korteweg type which allows for phase transitions. We show that…
In this paper, we develop a high order structure-preserving local discontinuous Galerkin (DG) scheme for the compressible self-gravitating Euler equations, which pose great challenges due to the presence of time-dependent gravitational…
The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical…