A fast algorithm for particle simulations
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
Journal of Computational Physics
Fourth-order symplectic integration
Physica D
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Numerical study on Landau damping
Physica D
A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow
Journal of Computational Physics
Plasma Physics Via Computer
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Darwin-Vlasov simulations of magnetised plasmas
Journal of Computational Physics
High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
Journal of Computational Physics
A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit
Journal of Scientific Computing
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
Journal of Computational Physics
Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Multi-GPU simulations of Vlasov's equation using Vlasiator
Parallel Computing
Journal of Scientific Computing
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 31.47 |
The Vlasov-Poisson equations describe the evolution of a collisionless plasma, represented through a probability density function (PDF) that self-interacts via an electrostatic force. One of the main difficulties in numerically solving this system is the severe time-step restriction that arises from parts of the PDF associated with moderate-to-large velocities. The dominant approach in the plasma physics community for removing these time-step restrictions is the so-called particle-in-cell (PIC) method, which discretizes the distribution function into a set of macro-particles, while the electric field is represented on a mesh. Several alternatives to this approach exist, including fully Lagrangian, fully Eulerian, and so-called semi-Lagrangian methods. The focus of this work is the semi-Lagrangian approach, which begins with a grid-based Eulerian representation of both the PDF and the electric field, then evolves the PDF via Lagrangian dynamics, and finally projects this evolved field back onto the original Eulerian mesh. In particular, we develop in this work a method that discretizes the 1+1 Vlasov-Poisson system via a high-order discontinuous Galerkin (DG) method in phase space, and an operator split, semi-Lagrangian method in time. Second-order accuracy in time is relatively easy to achieve via Strang operator splitting. With additional work, using higher-order splitting and a higher-order method of characteristics, we also demonstrate how to push this scheme to fourth-order accuracy in time. We show how to resolve all of the Lagrangian dynamics in such a way that mass is exactly conserved, positivity is maintained, and high-order accuracy is achieved. The Poisson equation is solved to high-order via the smallest stencil local discontinuous Galerkin (LDG) approach. We test the proposed scheme on several standard test cases.