A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

Crouseilles, Nicolas; Respaud, Thomas; Sonnendrücker, Éric

doi:10.1016/j.cpc.2009.04.024

Cited by 99 publications

(103 citation statements)

References 29 publications

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“…The DG method is running with N x = N v = 30 points and 5 Gauß points per cell enable to reconstruct a 4th order polynomial. In the linear regime, the L 2 -norm of the electric field is known to decay exponentially in time, the rate of which can be computed a priori (see [8,21]). In Table 1 the numerical decay rate together with the period of the oscillations are presented, for different values of the initial mode k. We observe that they are in a very good agreement with the linear theory.…”

Section: One-dimensional Landau Dampingmentioning

confidence: 99%

Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson

2011

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Abstract. We present a discontinuous Galerkin scheme for the numerical approximation of the onedimensional periodic Vlasov-Poisson equation. The scheme is based on a Galerkin-characteristics method in which the distribution function is projected onto a space of discontinuous functions. We present comparisons with a semi-Lagrangian method to emphasize the good behavior of this scheme when applied to Vlasov-Poisson test cases.Résumé. Une méthode de Galerkin discontinu est proposée pour l'approximation numérique de l'équation de Vlasov-Poisson 1D. L'approche est basée sur une méthode Galerkin-caractéristiques où la fonction de distribution est projetée sur un espace de fonctions discontinues. En particulier, la méthode est comparéeà une méthode semi-Lagrangienne pour l'approximation de l'équation de Vlasov-Poisson.

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Section: One-dimensional Landau Dampingmentioning

confidence: 99%

Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson

2011

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“…This method is compared to other reconstructions like those used in PFC or PPM approaches. We will also introduce a new method based on a cubic splines approximation of the unknown; the characteristics curves are followed forwardly as in [27,9], but the unknown is reconstructed in a conservative way using its values on the transported non-uniform mesh.…”

Section: Introductionmentioning

confidence: 99%

Conservative semi-Lagrangian schemes for Vlasov equations

Crouseilles

Mehrenberger

Sonnendrücker

2010

Journal of Computational Physics

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Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case, they present an alternative to the traditional semi-Lagrangian schemes which can suffer from bad mass conservation, in this time splitting setting.

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“…FD6) for computing the derivative using (14), with p = 4 (resp p = 6). We consider different discretizations in space: On Figure 1, we see the solution and error of H17, using ∆t = 2 −6 , N = 32 (top) and N = 64 (bottom) at time T = 20 that is after 10/π turns.…”

Section: Rotationmentioning

confidence: 99%

“…We call this classical semi-Lagrangian method BSL for backward semi-Lagrangian method. This is opposed in particular to CSL, conservative semi-Lagrangian methods, which solve the conservative form (1) of the Vlasov equation still with backward characteristics as in [11][12][13], and FSL, forward semi-Lagrangian methods introduced in [14] for the Vlasov equation, which solves the characteristics forward in time. There have also been works on positivity preserving conservative Discontinuous Galerkin methods [15,16] and also on semi-Lagrangian methods on adaptive grids based on wavelet interpolation [17,18], see also [19] for a convergence proof.…”

Section: Introductionmentioning

confidence: 99%

The semi-Lagrangian method on curvilinear grids

Hamiaz

Mehrenberger

Sellama

et al. 2016

Communications in Applied and Industrial Mathematics

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We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

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A forward semi-Lagrangian method for the numerical solution of the Vlasov equation

Cited by 99 publications

References 29 publications

Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson

Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson

Conservative semi-Lagrangian schemes for Vlasov equations

The semi-Lagrangian method on curvilinear grids

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