Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories
Résumé
In this work, we compare different interpolation operators in the context of particle track-
ing with an emphasis on situations involving velocity field with steep gradients. Since, in
this case, most classical methods give rise to the Gibbs phenomenon (generation of oscil-
lations near discontinuities), we present new methods for particle tracking based on sub-
division schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which
has shown its advantage in image processing in presence of strong contrasts. First an ana-
lytic univariate case with a discontinuous velocity field is considered in order to highlight
the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are pro-
vided. Then, we show, regardless of the interpolation method, the need to use a conserva-
tive approach when integrating a conservative problem with a velocity field deriving from
a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent
potential encountered in the edge turbulence of magnetically confined plasmas, to com-
pare the propagation of density structures (turbulence bursts) with the dynamics of test
particles. This study highlights the difference between particle transport and density trans-
port in turbulent fields.