Journal of Computational Physics
A finite element code for the simulation of one-dimensional Vlasov plasmas I. Theory
Journal of Computational Physics
A finite element code for the simulation of one-dimensional Vlasov plasmas. II.Applications
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Performance and optimization of direct implicit particle simulation
Journal of Computational Physics
Fourth-order symplectic integration
Physica D
Order conditions for canonical Runge-Kutta schemes
SIAM Journal on Numerical Analysis
A splitting algorithm for Vlasov simulation with filamentation filtration
Journal of Computational Physics
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Numerical study on Landau damping
Physica D
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
A numerical scheme for the integration of the Vlasov--Maxwell system of equations
Journal of Computational Physics
Numerical modelling of the two-dimensional Fourier transformed Vlasov-Maxwell system
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
Journal of Computational Physics
A new conservative unsplit method for the solution of the Vlasov equation
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
Block-structured adaptive mesh refinement algorithms for Vlasov simulation
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.45 |
In this paper, we propose energy-conserving numerical schemes for the Vlasov-Ampere (VA) systems. The VA system is a model used to describe the evolution of probability density function of charged particles under self consistent electric field in plasmas. It conserves many physical quantities, including the total energy which is comprised of the kinetic and electric energy. Unlike the total particle number conservation, the total energy conservation is challenging to achieve. For simulations in longer time ranges, negligence of this fact could cause unphysical results, such as plasma self heating or cooling. In this paper, we develop the first Eulerian solvers that can preserve fully discrete total energy conservation. The main components of our solvers include explicit or implicit energy-conserving temporal discretizations, an energy-conserving operator splitting for the VA equation and discontinuous Galerkin finite element methods for the spatial discretizations. We validate our schemes by rigorous derivations and benchmark numerical examples such as Landau damping, two-stream instability and bump-on-tail instability.