Vlasov simulations using velocity-scaled Hermite representations
The authors investigate the efficiency, accuracy, and stability of two different pseudo-spectral methods using scaled Hermite basis and weight functions, applied to the nonlinear Vlasov-Poisson equations in one dimension \((1d-1v)\). A variable velocity scale \(U\) is introduced into the Hermite basis and is shown to yield orders of magnitude reduction in errors, as compared to linear kinetic theory, with no increase in workload. A set of Fourier-Hermite coefficients, representing a periodic Gaussian distribution function, are advanced through time with an \(O(\Delta t^2)\)-accurate splitting method. Within this splitting scheme, the advection and acceleration terms of the Vlasov equation are solved separately using an \(O(\Delta t^4)\)-accurate Runge-Kutta method. Damping and growth rates, oscillation frequencies, \(E\)-field saturation levels, and phase-space evolution are seen to be qualitatively correct during simulations.
scientific article; zbMATH DE number 1282701