Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma

Abstract

We propose an Hermite spectral method for the Fokker-Planck-Landau (FPL) equation. Both the distribution functions and the collision terms are approximated by series expansions of the Hermite functions. To handle the complexity of the quadratic FPL collision operator, a reduced collision model is built by adopting the quadratic collision operator for the lower-order terms and the diffusive Fokker-Planck operator for the higher-order terms in the Hermite expansion of the reduced collision operator. The numerical scheme is split into three steps according to the Strang splitting, where different expansion centers are employed for different numerical steps to take advantage of the Hermite functions. The standard normalized Hermite basis [36] is adopted during the convection and collision steps to utilize the precalculated coefficients of the quadratic collision terms, while the one constituted by the local macroscopic velocity and temperature is utilized for the acceleration step, by which the effect of the external force can be simplified to an ODE. Projections between different expansion centers are achieved by an algorithm proposed in [29]. Several numerical examples are studied to test and validate our new method

References in corpus (7)

• A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources
• Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
• Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
• High Order Maximum Principle Preserving Semi-Lagrangian Finite Difference WENO schemes for the Vlasov Equation
• Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit
• A Conservative Scheme for Vlasov Poisson Landau modeling collisional plasmas
• Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation

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• Relaxation model for a homogeneous plasma with spherically symmetric velocity space
• A spectral collocation method for the Landau equation in plasma physics