We apply a second-order semi-Lagrangian spectral method for the Vlasov–Poisson system, by implementing Hermite functions in the approximation of the distribution function with respect to the velocity variable. Numerical tests are performed on a standard benchmark problem, namely the two-stream instability test case. The approach uses two independent sets of Hermite functions, based on Gaussian weights symmetrically placed with respect to the zero velocity level. An experimental analysis is conducted to detect a reasonable location of the two weights in order to improve the approximation properties.
On the Use of Hermite Functions for the Vlasov–Poisson System / Fatone, Lorella; Funaro, Daniele; Manzini, Gianmarco. - 134:(2020), pp. 143-153. (Intervento presentato al convegno 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 tenutosi a Londra nel 9-13 Luglio 2018) [10.1007/978-3-030-39647-3_10].
On the Use of Hermite Functions for the Vlasov–Poisson System
Daniele Funaro;
2020
Abstract
We apply a second-order semi-Lagrangian spectral method for the Vlasov–Poisson system, by implementing Hermite functions in the approximation of the distribution function with respect to the velocity variable. Numerical tests are performed on a standard benchmark problem, namely the two-stream instability test case. The approach uses two independent sets of Hermite functions, based on Gaussian weights symmetrically placed with respect to the zero velocity level. An experimental analysis is conducted to detect a reasonable location of the two weights in order to improve the approximation properties.
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