Comparison of different interpolation operators including nonlinearsubdivision schemes in the simulation of particle trajectories

International audienceIn 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, inthis 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 whichhas 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 highlightthe 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 froma potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependentpotential encountered in the edge turbulence of magnetically confined plasmas, to com-pare the propagation of density structures (turbulence bursts) with the dynamics of testparticles. This study highlights the difference between particle transport and density trans-port in turbulent fields