Numerical comparisons of gyrokinetic multi-water-bag models

Coulette, David; Besse, Nicolas

doi:10.1016/j.jcp.2013.03.065

Cited by 15 publications

(26 citation statements)

References 16 publications

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“…PPM2), p = 17 which corresponds to LAGH17, and Lauritzen which corresponds to the reconstruction proposed in [14]. One can observe that the linear part is well reproduced by all the method since the instability rate of all the methods is very close to the analytical one proposed by [4].…”

Section: Numerical Resultsmentioning

confidence: 63%

“…The growth rate can be obtained by a generalization of the approach performed in [4]. Hence, growth rates obtained in [4] can be compared to numerical results.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The growth rate can be obtained by a generalization of the approach performed in [4]. Hence, growth rates obtained in [4] can be compared to numerical results. The total mass M(t) is preserved by the model and it is an important point for the methods to preserve this quantity as much as possible.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We then consider a 4D drift-kinetic slab simulation [10], [4] which can be viewed as a polar guiding-center equation of type (1) coupled with a Vlasov type equation in the parallel (z, v) direction. In these two configurations, some first results of a new conservative semi-Lagrangian method are given and compared to the standard one [10].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence

et al. 2014

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Abstract. While developing a new semi-Lagrangian solver, the gap between a linear Landau run in 1D×1D and a 5D gyrokinetic simulation in toroidal geometry is quite huge. Intermediate test cases are welcome for testing the code. A new fully two-dimensional conservative semi-Lagrangian (CSL) method is presented here and is validated on 2D polar geometries. We consider here as building block, a 2D guiding-center type equation on an annulus and apply it on two test cases. First, we revisit a 2D test case previously done with a PIC approach [18] and detail the boundary conditions. Second, we consider a 4D drift-kinetic slab simulation (see [10]). In both cases, the new method appears to be a good alternative to deal with this type of models since it improves the lack of mass conservation of the standard semi-Lagrangian (BSL) method.

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Section: Numerical Resultsmentioning

confidence: 63%

“…The growth rate can be obtained by a generalization of the approach performed in [4]. Hence, growth rates obtained in [4] can be compared to numerical results.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence

et al. 2014

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“…In the uniform case, we are able to check the linear phase behaviour by solving numerically the dispersion relation and compare the simulation output with it (see also [25,26]). Note that the dispersion relation depends on k : this permits to compare simulations in the oblique and uniform case, in order to check the correctness of the simulations in the oblique case, as we will see.…”

Section: Comparison With Classical (Not Aligned) Approachmentioning

confidence: 99%

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

et al. 2017

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This work is devoted to the study of field-aligned interpolation in semi-Lagrangian codes. In the context of numerical simulations of magnetic fusion devices, this approach is motivated by the observation that gradients of the solution along the magnetic field lines are typically much smaller than along a perpendicular direction. In toroidal geometry, fieldaligned interpolation consists of a 1D interpolation along the field line, combined with 2D interpolations on the poloidal planes (at the intersections with the field line). A theoretical justification of the method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). In the first case, the algorithm is implemented in Selalib (semi-Lagrangian library), and the numerical simulations provide linear growth rates that are in accordance with the linear dispersion analysis. In the second case, the algorithm is implemented in the Gysela code, and the numerical simulations are benchmarked with those employing the standard (not aligned) scheme. Numerical experiments show that field-aligned interpolation leads to considerable memory savings for the same level of accuracy; substantial savings are also expected in reactor-scale simulations.

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An exponential integrator for the drift-kinetic model

Crouseilles

Einkemmer

Prugger

2018

Computer Physics Communications

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We propose an exponential integrator for the drift-kinetic equation in cylindrical geometry. This approach removes the CFL condition from the linear part of the system (which is often the most stringent requirement in practice) and treats the remainder explicitly using Arakawa's finite difference scheme. The present approach is mass conservative, up to machine precision, and significantly reduces the computational effort per time step.In addition, we demonstrate the efficiency of our method by performing numerical simulations in the context of the ion temperature gradient instability. In particular, we find that our numerical method can take time steps comparable to what has been reported in the literature for the (predominantly used) splitting approach. In addition, the proposed numerical method has significant advantages with respect to conservation of energy and efficient higher order methods can be obtained easily. We demonstrate this by investigating the performance of a fourth order implementation. arXiv:1705.09923v2 [physics.comp-ph] 1 Sep 2017

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Numerical comparisons of gyrokinetic multi-water-bag models

Cited by 15 publications

References 16 publications

A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence

A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence

Field-Aligned Interpolation for Semi-Lagrangian Gyrokinetic Simulations

An exponential integrator for the drift-kinetic model

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