Space-only hyperbolic approximation of the Vlasov equation

We construct an hyperbolic approximation of the Vlasov equation in which the dependency on the velocity variable is removed. The resulting model enjoys interesting conservation and entropy properties. It can be numerically solved by standard schemes for hyperbolic systems. We present numerical results for one-dimensional classical test cases in plasma physics: Landau damping, two-stream instability

[1]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[2]  E. Sonnendrücker,et al.  Comparison of Eulerian Vlasov solvers , 2003 .

[3]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[4]  Jean-Marc Hérard,et al.  A LOCAL TIME-STEPPING DISCONTINUOUS GALERKIN ALGORITHM FOR THE MHD SYSTEM , 2009 .

[5]  David Tskhakaya,et al.  Optimization of PIC codes by improved memory management , 2007, J. Comput. Phys..

[6]  Virginie Grandgirard,et al.  Gyrokinetic Semi-lagrangian Parallel Simulation Using a Hybrid OpenMP/MPI Programming , 2007, PVM/MPI.

[7]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[8]  Anaïs Crestetto.  Optimisation de méthodes numériques pour la physique des plasmas : application aux faisceaux de particules chargées , 2012 .

[9]  Timothy J. Barth,et al.  On Discontinuous Galerkin Approximations of Boltzmann Moment Systems With Levermore Closure , 2006 .

[10]  Solène Le Bourdiec,et al.  Numerical solution of the Vlasov-Poisson system using generalized Hermite functions , 2006, Comput. Phys. Commun..

[11]  Bengt Eliasson.  Outflow Boundary Conditions for the Fourier Transformed One-Dimensional Vlasov–Poisson System , 2001, J. Sci. Comput..

[12]  Eric Sonnendrücker,et al.  Conservative semi-Lagrangian schemes for Vlasov equations , 2010, J. Comput. Phys..

[13]  B. Perthame,et al.  Boltzmann type schemes for gas dynamics and the entropy property , 1990 .