1 / 13

Recent results with Goddard AMR codes

Recent results with Goddard AMR codes. Dae-Il (Dale) Choi NASA/Goddard, USRA Collaborators J. Centrella, J. Baker, J. van Meter, D. Fiske, B. Imbiriba (NASA/Goddard) J. D. Brown and L. Lowe (NCSU) Supported by NASA ATP02-0043-0056 PSU NR Lunch, APR 29, 2004. Outline. Codes/Features

aman
Download Presentation

Recent results with Goddard AMR codes

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. Recent results with Goddard AMR codes Dae-Il (Dale) Choi NASA/Goddard, USRA Collaborators J. Centrella, J. Baker, J. van Meter, D. Fiske, B. Imbiriba (NASA/Goddard) J. D. Brown and L. Lowe (NCSU) Supported by NASA ATP02-0043-0056 PSU NR Lunch, APR 29, 2004

  2. Outline • Codes/Features • Summary of past and present works • Brill waves • Binary black holes • Future

  3. Codes • “Hahndol” (= “One-Stone”= “Ein-stein” in Korean) • Vacuum Evolution code: 3+1 BSSN. • Free evolution (BSSN gauges imposed). • FMR, AMR and Parallel (Paramesh): scalability good. • Puncture BHs, Waves. • AMRMG_3D(NCSU) • Elliptic solver: Multi-grid. • Parallel, AMR support based on Paramesh. • Initial data generator: Brill wave, 2BH, single distorted BH.

  4. Key Features: Simplicity • Simple grid structure: A hierarchy of the logically cartesiangrid blocks with identicalstructure. Considerably simplified data structure is known at compile time. • Simple tree structure: Grid blocks are managed by simple tree structure which tracks the spatial relationships between blocks. • Mesh refinement is“block-based” and uses“bisection”method (De Zeeuw & Powell, 1993) • Block is a basic “unit” for mesh-refinement and domain decomposition. • No clusterer needed. • Simple communication patterns: Blocks are distributed amongst available processors in ways which maximize block locality and minimize inter-processor communications.  May be crucial for parallel implementation

  5. Mesh Refinement Works • Fixed Mesh Refinement (FMR) • Study of refinement interface conditions with linear waves [JCP 193, 398 (2004) (physics/0307036)] • Key Ideas: Quadratic interpolation combined with “flux” matching guarantees 2nd order convergence and minimizes interface noises. • Single puncture BH: thoroughconvergence study with 8 levels of FMR [gr-qc/0403048]. • Key results: OB at ~100M, high resolution (h ~ 1/64) near puncture. • Already very helpful in 2BH simulations [work in progress]. • Distorted BH [work in progress, D. Fiske]. • Adaptive Mesh Refinement (AMR) • Weak GW simulations [PRD 62, 084039 (2000)] • 2-level; fine grid tracking the waves. • Brill wave simulations [work in progress] • Zooming into critical regime.

  6. Brill Waves • Initial Data: Time symmetric (axi-symmetric) Brill wave solution. • B.C.: Octant + Sommerfeld outgoing except . • First order shock avoidance slicing [M. Alcubierre, CQG 20, 607 (2003)], . • AMR interface conditions: 2nd order interpolation followed by “flux” matching  matching function and first derivatives of function. • Adaptive regridding based on the first derivatives of variables. • Physics: find the critical parameter, A*, and study the critical phenomena (& later, extend to non-axisymmetry). • Previous estimate of the critical parameter: 4.7 < A*< 5.0 [M. Alcubierre, et al, PRD 61, 041501 (2000), Use 128^3 grids ]. • Hahndol: Zooming into critical regime: current estimation  4.80 < A* < 4.85.

  7. Brill Wave: Preliminary results • Dispersal for A < 4.8 • Lapse collapses for A > 4.85 • 4.8 < A* < 4.85: results are sensitive to various parameters such as location of outer boundary and resolution.

  8. Brill Wave: Preliminary Results • A = 4.84 • 64 x 64 x 64 base grid (h~0.125) • 3 additional levels  finest resolution = 0.015625 (effective resolution of 512 x 512 x 512 unigrid) • Snapshots for lapse (on Z=0 plane) • Working on to find AH to confirm BH formation. • Caution: Inadequate resolution may give completely wrong outcome! • Run with only 2 additional levels results in dispersal (finest resolution = 0.3125) • Further study is under way.

  9. Binary Black Hole Simulation (Head-on collision) • Initial Data (time = 0) • Simple cases can be done by hand: two equal mass non-spinning black holes with zero initial velocity. • Spatial metric on 3d spacelike hypersurface, • Evolution (time > 0) • Lapse condition (1+log) • Shift condition (Hyperbolic driver) • Mesh Refinement • Source region: scale ~ M, put more grid points. • Wavezone: scale ~ (10--100)M, put less grid points. • Boundary of computational domain: ~ a few hundred M.

  10. Binary Black Hole Simulations (Mesh Structure)Mesh Refinement allows one to put outer boundary as far as possible.Efficient distribution of grid points: more near black holes.

  11. BBH Head-on collision • Initial separation = 5M, M=2, Two event horizons initially separated. • Mesh refinement calculations. (OB at 120M) • gxx on Z=0 plane. • Gauge wave followed by physical wave.

  12. BBH Head-on collision • Coordinate conditions [gtx, gtt]. • Two black hole merges into a single black hole. • Gauge wave comes out first. • Assume profile of a single black hole after merger.

  13. Future • Attacking both “astrophysics” and “physics” problems. • Astrophysics: orbiting black hole binaries, distorted black holes  gravitational wave astrophysics. • Physics: Brill wave, etc. • Analysis tools for mesh refinement • Horizon finders • Invariants, GW extraction • Focus on LISA source modeling: GW extraction for black holes binaries  Data analysis.

More Related