Journal of Computational Physics
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
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
Darwin-Vlasov simulations of magnetised plasmas
Journal of Computational Physics
A new conservative unsplit method for the solution of the Vlasov equation
Journal of Computational Physics
Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov-Maxwell system
Journal of Computational Physics
Parallelization of a Vlasov-Maxwell solver in four-dimensional phase space
Parallel Computing
VALIS: A split-conservative scheme for the relativistic 2D Vlasov-Maxwell system
Journal of Computational Physics
Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality
Journal of Computational Physics
Scalable Direct Vlasov Solver with Discontinuous Galerkin Method on Unstructured Mesh
SIAM Journal on Scientific Computing
Block-structured adaptive mesh refinement algorithms for Vlasov simulation
Journal of Computational Physics
Hi-index | 31.48 |
A common problem with direct Vlasov solvers is ensuring that the distribution function remains positive. A related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space. In this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for Eulerian split approaches to Vlasov solvers. From these tests we conclude that maintaining positivity is less important than correctly dissipating the fine-scale structure which arises naturally in the solution to many Vlasov problems. Furthermore we show that there are distinct advantages to using high-order schemes, i.e., third order rather than second. A natural choice which satisfies all of these requirements is the piecewise parabolic method (PPM), which is applied here to Vlasov's equation for the first time.