Multi-Moment Advection scheme for Vlasov simulations

Abstract

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one- and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.

52 pages, 18 figures, accepted for the publication in Journal of Computational Physics

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• A Forward semi-Lagrangian Method for the Numerical Solution of the Vlasov Equation
• Electron Shock Surfing Acceleration in Multidimensions: Two-dimensional Particle-In-Cell Simulation of Collisionless Perpendicular Shock
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Cited by in corpus (5)

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• Quadratic conservative scheme for relativistic Vlasov--Maxwell system
• Multidimensional VlasovPoisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes
• Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma