A method of local corrections for computing the velocity field due to a distribution of vortex blobs
Journal of Computational Physics
A fast algorithm for particle simulations
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
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Blob method for kinetic plasma simulation with variable-size particles
Journal of Computational Physics
Grid and particle hydrodynamics: beyond hydrodynamics via fluid element particle-in-cell
Journal of Computational Physics
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
The constrained interpolation profile method for multiphase analysis
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
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
Plasma Physics Via Computer
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Fragmentation, merging, and internal dynamics for PIC simulation with finite size particles
Journal of Computational Physics
High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
Journal of Computational Physics
Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
An Eulerian-Lagrangian WENO finite volume scheme for advection problems
Journal of Computational Physics
Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation
Journal of Computational Physics
Multi-GPU simulations of Vlasov's equation using Vlasiator
Parallel Computing
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Hi-index | 31.48 |
In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially non-oscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear hyperbolic equations, can be factored into right and left flux matrices. It is the factoring of the interpolation matrices which makes it possible to apply the WENO methodology in the reconstruction used in the semi-Lagrangian update. The spatial WENO reconstruction developed for this method is conservative and updates point values of the solution. While the third, fifth, seventh and ninth order reconstructions are presented in this paper, the scheme can be extended to arbitrarily high order. WENO reconstruction is able to achieve high order accuracy in smooth parts of the solution while being able to capture sharp interfaces without introducing oscillations. Moreover, the CFL time step restriction of a regular finite difference or finite volume WENO scheme is removed in a semi-Lagrangian framework, allowing for a cheaper and more flexible numerical realization. The quality of the proposed method is demonstrated by applying the approach to basic test problems, such as linear advection and rigid body rotation, and to classical plasma problems, such as Landau damping and the two-stream instability. Even though the method is only second order accurate in time, our numerical results suggest the use of high order reconstruction is advantageous when considering the Vlasov-Poisson system.