1 / 47

Context

The waterbag method and Vlasov-Poisson equations in 1D: some examples S. Colombi (IAP, Paris) J. Touma (CAMS, Beirut). Context. Tradition: N -body - Poor resolution in phase-space N –body relaxation Aims : direct resolution in phase-space.

constance-murray
Download Presentation

Context

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The waterbag method and Vlasov-Poisson equations in 1D: some examplesS. Colombi (IAP, Paris)J. Touma (CAMS, Beirut)

  2. Context • Tradition:N-body - Poor resolution in phase-space • N–body relaxation • Aims : direct resolution in phase-space. • Now (almost ?) possible in with modern supercomputers • Here: 1D gravity (2D phase-space) 6D

  3. Phase-space of a N-body simulation v Holes Suspect résonance x

  4. Note : The waterbag method is very old Etc…

  5. The waterbag method • Exploits directly the fact that f[q(t),p(t),t]=constant along trajectories • Suppose that f(q,p) independent of (q,p) in small patches (waterbags) (optimal configuration: waterbags are bounded by isocontours of f) • It is needed to follow only the boundary of each patch, which can be sampled with an oriented polygon • Polygons can be locally refined in order to give account of increasing complexity

  6. Dynamics of sheets: 1D gravity • Force calculation is reduced to a contour integral

  7. Filamentation: need to add more and more points

  8. Stationnary solution (Spitzer 1942) t=0

  9. t=300

  10. Ensemble of stationnary profiles

  11. Relaxation of a Gaussian Few contours Many contours

  12. Merger of 2 stationnary

  13. Energy conservation

  14. Pure waterbags: convergence study toward the cold case

  15. Quasi stationary waterbag

  16. Projected density: Singularity in r-2/3 Projected density: Singularity in r-1/2

  17. The structure of the core

  18. The logarithmic slope of the potential: Convergence study

  19. Energy conservation Phase space volume conservation

  20. Adiabatic invariant

  21. Energies

  22. Establishment of the central density profile: f=f0E-5/6 (Binney, 2004)

  23. Effet of random perturbations

  24. Energy conservation Phase space volume conservation

  25. Effect of the perturbations on the slope

  26. Refinement during runtime TVD interpolation (no creation of artificial curvature terms) The curvature is changing sign Normal case Note: in the small angle regime :

  27. Time-step: standard Leapfrog(or predictor corrector if varying time step)

  28. Better sampling of initial conditions: Isocontours • Construction of the oriented polygon following isocontours of f using the marching cube algorithm • Contour distribution computed such that the integral of (fsampled-ftrue)2 is bounded by a control parameter

  29. Stationary solution (Spitzer 1942) Total mass Total energy

More Related