Journal of Computational Physics
Multi-scale particle-in-cell plasma simulation
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Flux-corrected transport I. SHASTA, a fluid transport algorithm that works
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
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
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Numerical study on Landau damping
Physica D
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
Journal of Computational Physics
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
SIAM Journal on Scientific Computing
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
Full f gyrokinetic method for particle simulation of tokamak transport
Journal of Computational Physics
A high-order finite-volume algorithm for Fokker-Planck collisions in magnetized plasmas
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
Journal of Computational Physics
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we propose a new conservative hybrid finite element-finite difference method for the Vlasov equation. The proposed methodology uses Strang splitting to decouple the nonlinear high dimensional Vlasov equation into two lower dimensional equations, which describe spatial advection and velocity acceleration/deceleration processes respectively. We then propose to use a semi-Lagrangian (SL) discontinuous Galerkin (DG) scheme (or Eulerian Runge-Kutta (RK) DG scheme with local time stepping) for spatial advection, and use a SL finite difference WENO for velocity acceleration/deceleration. Such hybrid method takes the advantage of DG scheme in its compactness and its ability in handling complicated spatial geometry; while takes the advantage of the WENO scheme in its robustness in resolving filamentation solution structures of the Vlasov equation. The proposed highly accurate methodology enjoys great computational efficiency, as it allows one to use relatively coarse phase space mesh due to the high order nature of the scheme. At the same time, the time step can be taken to be extra large in the SL framework. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and classical plasma problems, such as Landau damping and the two stream instability. Although we only tested 1D1V examples, the proposed method has the potential to be extended to problems with high spatial dimensions and complicated geometry. This constitutes our future research work.