On the use of Hermite functions for the Vlasov-Poisson system. (English) Zbl 1484.65247
Sherwin, Spencer J. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2018. Selected papers from the ICOSAHOM conference, London, UK, July 9–13, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 134, 143-153 (2020).
Summary: 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.
For the entire collection see [Zbl 1462.65006].
For the entire collection see [Zbl 1462.65006].
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
| 35Q83 | Vlasov equations |
| 35Q35 | PDEs in connection with fluid mechanics |
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