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
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
Journal of Computational Physics
The constrained interpolation profile method for multiphase analysis
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
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
Journal of Computational Physics
A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
Journal of Computational Physics
Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
SIAM Journal on Scientific Computing
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
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
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
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 Scientific Computing
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Hi-index | 31.46 |
Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community [29,3,4,18,32,5,24,26]. In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [6], as a way to decouple the nonlinear Vlasov system into a sequence of 1-D advection equations, each of which has an advection velocity that only depends on coordinates that are transverse to the direction of propagation. To evolve the decoupled linear equations, we propose to couple the SL framework with the semi-discrete DG formulation. The proposed SL DG method is free of time step restriction compared with the Runge-Kutta DG method, which is known to suffer from numerical time step limitation with relatively small CFL numbers according to linear stability analysis. We apply the recently developed positivity preserving (PP) limiter [37], which is a low-cost black box procedure, to our scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. We analyze the stability and accuracy properties of the SL DG scheme by establishing its connection with the direct and weak formulations of the characteristics/Lagrangian Galerkin method [23]. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and via classical plasma problems, such as Landau damping and the two stream instability.