Study of (Puncture) Black Holes

Jan 28, 2005: "Standard" headon collision

• The following movie [[MPEG] gcxx along x-axis] shows some important points.
  • Red line uses lapse gauge condition with Psi_{BL} factor, blue line without Psi_{BL} factor (parameter files on columbia for them /nobackup13/jvanmete/s8_headon_l3_bare/id0 and /nobackup13/jvanmete/s8_headon_l3_bare_r2/id0 respectively). Blue run still running now.
  • First point: With the BL factor, there is less dynamics initially, so better convergence initially (which I showed already several meetings ago) than the case without the BL factor. However, later times, metrik grows crazy for the case with the BL factor compared to the case without the BL factor [[PS] max(gcxx) vs. Zeit]. That is *why* the runs with the BL factor crashes!! Look at the movie again. =)
  • Above run has h_f=0.0375 = 1/26.666667. Since we are convinced that at least for headon run we like to do, the right lapse condition is the one without BL fact, we need do a thorough convergence testing (before we test with excision). For high resolutoin, we may need excision anyway, but we need to push for convergence testing as much as possible without excision.
  • First, we need to establish convergence of constraints, HC MC, etc. Then, also check invariatns, etc. Finally, *if* we can achieve long term evolution even for high resolution, then we need to check convergence on waveforms as well!
• Main point I want to make here is that we really need to carefully analysize the data from a long term behavior of the runs. My originally conclusion about which gauge is better was based only on a short initial time data. Which was worse later time crashing the code prematurely. Max (gcxx) graph I have above shows this point. Things are better for the case with BL factor initially, but later, it gets worse than the other case.
• Another motivation to finish up non-excision runs is to take them as test-beds for excision runs.

[Recent results Dec 28, 2004] "Standard" headon collision

• Convergence plots
  • Zero shift
    • 1+log w/o Psi_{BL} [Hamiltonian along x-axis ([PostScript])]
    • 1+log with Psi_{BL} [To be added]
    
    
  • non zero shift (hyperbolic Gamma driver)
    • 1+log w/o Psi_{BL} [Hamiltonian along x-axis ([PostScript])]
    • 1+log with Psi_{BL} [To be added]

Presentations and Papers (As of Sep 2003):

• Poster Presentation [PS file] and Article for Proceedings [PS file] at Chicago Workshop on Adaptive Mesh Refinement Methods, Sept 3--5, 2003, Chicago, IL
  

Results (Test runs with binary black holes in April 2004):

MPEG Movies for head-on collision (equal mass, non-spinning, initially at rest) [lapse] [shift_x] [gxx_wide] [gxx_zoomin]

Results (Test runs done in Aug-Nov 2003):

• Single BH at (0,0,0) with "1+log" slicing, and zero shift
  
  • NEW JAN 8, 2004 8-Level FMR (QUAD+REFLUX)--- The interface boundaries are at (1M,2M,4M,8M,16M,32M,64M)
    HCE Convergence Plots [t=13.75(PS)] [t=13.75(PS)(around x=4M)]
    gxx, lapse, trck Plots [t=13.75(PS)(x=0~7)]
    
  • 6-Level FMR (QUAD+REFLUX)
    MPEG Movies (Resolution Level = 0) [gxx] [kxx] [trck] [lapse] [ccfx] [HCE]
    MPEG Movies (Resolution Level = 1) [gxx] [kxx] [trck] [lapse] [ccfx] [HCE]
    MPEG Movies (Resolution Level = 2) [gxx, gxx big] [lapse, lapse big]
    HCE Convergence Plots (WRONG, TO BE UPDATED) [t=1.5(PS)] [t=5.9(PS)] [t=12(PS)] [t=20] (PS)]
    
  
  
• Single BH at (0,0,0) with "1+log" slicing, long.. time test
  
  • Unigrid:
    Domain: [0,5.12]
    DIR: 1plog/uni_test/32_ilapse7/ (h=0.16)
    1plog/uni_test/64_ilapse7/ (h=0.08)
    1plog/uni_test/128_ilapse7/ (h=0.04)
    Plots: [lapse] (PDF) [gxx/psi_BL^4] (PDF) [H.C.E] (PDF)
    Results:
    
• Single BH at (0,0,0) with "1+log" slicing, short time test
  
  • Unigrid:
    Domain: [0,2.5]
    DIR: 1plog/hce_test/16/ (h=0.15625)
    1plog/hce_test/32/ (h=0.078125)
    1plog/hce_test/64/ (h=0.039065)
    1plog/hce_test/128/ (h=0.019532)
    Plots: [lapse] (PDF) [gxx/psi_BL^4] (PDF) [H.C.E] (PDF)
    Results: * Outer boundary error coming in (See H.C.E).
    * converging 2nd order as resolution is increased maybe except very close to the puncture!
    
  • FMR:
    Domain: [0,2.5]
    Dir: 1plog/test_aug_12_2003/16_f/ h=0.07813(0,1.25), 2*h(1.25,2.5)
    1plog/test_aug_12_2003/32_f/ h/2 (0,1.25), h (1.25,2.5)
    1plog/test_aug_12_2003/64_f/ h/4 (0,1.25), h/2(1.25,2.5)
    1plog/test_aug_12_2003/128_f/ h/8 (0,1.25), h/4(1.25,2.5)
    Plots: [lapse] (PDF) [gxx/psi_BL^4] (PDF) [H.C.E] (PDF)
    
• Binary Head-on Collision runs:
  
  • Equal Mass BH:
    • Lapse (AMR run): Time= [4 (PS)] [8 (PS)] [16 (PS)] [24 (PS)] [32 (PS)]
    • Metric variable g_xx (AMR run): Time= [4 (PS)] [8 (PS)] [16 (PS)] [24 (PS)] [32 (PS)]
  • Unequal Mass BH:
    • Lapse (AMR run): Time= [4 (PS)] [8 (PS)] [16 (PS)] [24 (PS)]
    • Metric variable g_xx (AMR run): Time= [4 (PS)] [8 (PS)] [16 (PS)] [24 (PS)]
• Binary Grazing Collision runs: Working on it...
  

• Puncture Issues
  • check why compu_trck_dot.F90 doesn't have puncture split in it.
• Shift Issues
  • talk to M. Anderson about his experiments with advection terms
  • Chuck Evan thesis to see how advection terms were handled.
  • C. Hirsch Ch17.2,etc to see comparions bet. centered differencin and upwiding...