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Simple Radiative Transfer in Decomposed Domains

Simple Radiative Transfer in Decomposed Domains. Tobi Heinemann Åke Nordlund Axel Brandenburg Wolfgang Dobler. The Pencil Code. High order finite difference code for MHD 6 th order in space, 3 rd order in time Memory and cache efficient Typical applications MHD turbulence Convection

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Simple Radiative Transfer in Decomposed Domains

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  1. Simple Radiative Transfer in Decomposed Domains Tobi Heinemann Åke Nordlund Axel Brandenburg Wolfgang Dobler

  2. The Pencil Code • High order finite difference code for MHD • 6th order in space, 3rd order in time • Memory and cache efficient • Typical applications • MHD turbulence • Convection • Accretion discs • Massive parallelization with MPI (Message Passing Interface)

  3. Radiative Transfer in Decomposed Domains • RT important for optically thin media • Diffusion approximation(s) deficient • RT is a highly non-local problem • Difficult to reconcile with domain decomposition

  4. The Transfer Equation & Parallelization Processors Analytic Solution:

  5. Intrinsic Calculation Ray direction The Transfer Equation & Parallelization Processors Analytic Solution:

  6. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  7. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  8. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  9. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  10. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  11. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  12. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  13. Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors

  14. Analytic Solution: Intrinsic Calculation Ray direction The Transfer Equation & Parallelization Processors

  15. Details about the implementation • Plasma composed of H and He • Only hydrogen ionization • Only H- opacity, calculated analytically No need for look-up tables • Ray directions determined by grid geometry No interpolation is needed

  16. Preliminary Results • 2D model of surface convection • Started from uniform initial state

  17. Preliminary Results • 3D model of sunspot • Started from Nordlund-Stein snapshot • Uniform initial magnetic field added

  18. Preliminary Results • 3D model of sunspot Bottom Surface

  19. Timing results • With 6 rays, and with ionization: 42.7 ms/pt/st • With 2 rays, and with ionization: 37.6 ms/pt/st • No radiation, but with ionization: 19.6 ms/pt/st • No radiation, and no ionization: 8.7 ms/pt/st • Ionization 2.3 times slower! • Radiation either 1.9 or 2.2 times slower.

  20. Conclusions The method • is conceptually simple • is robust (analytic expressions, not limited by table bounds) • has the potential to scale well in parallel environments

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