Simple Radiative Transfer in Decomposed Domains

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

description

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 - PowerPoint PPT Presentation

Transcript of Simple Radiative Transfer in Decomposed Domains

Page 1: Simple Radiative Transfer in Decomposed Domains

Simple Radiative Transfer in Simple Radiative Transfer in Decomposed DomainsDecomposed Domains

Tobi HeinemannÅke Nordlund

Axel Brandenburg

Wolfgang Dobler

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The Pencil CodeThe 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)

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Radiative Transfer in Radiative Transfer in Decomposed DomainsDecomposed Domains

• RT important for optically thin media

• Diffusion approximation(s) deficient

• RT is a highly non-local problem

• Difficult to reconcile with domain decomposition

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The Transfer Equation & The Transfer Equation & ParallelizationParallelization

Analytic Solution:Processors

Page 5: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Intrinsic Calculation

Processors

Page 6: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 7: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 8: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 9: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 10: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 11: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParParaallelizationllelization

Analytic Solution:

Ray direction

Communication

Processors

Page 12: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParallelizationParallelization

Analytic Solution:

Ray direction

Communication

Processors

Page 13: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParallelizationParallelization

Analytic Solution:

Ray direction

Communication

Processors

Page 14: Simple Radiative Transfer in Decomposed Domains

The Transfer Equation & The Transfer Equation & ParallelizationParallelization

Analytic Solution:

Ray direction

Processors

Intrinsic Calculation

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Details about the Details about the implementationimplementation

• 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

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Preliminary ResultsPreliminary Results

• 2D model of surface convection– Started from uniform initial state

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Preliminary ResultsPreliminary Results

• 3D model of sunspot– Started from Nordlund-Stein snapshot– Uniform initial magnetic field added

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Preliminary ResultsPreliminary Results

• 3D model of sunspot

Bottom Surface

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Timing resultsTiming results

• With 6 rays, and with ionization: 42.7 s/pt/st

• With 2 rays, and with ionization: 37.6 s/pt/st

• No radiation, but with ionization: 19.6 s/pt/st

• No radiation, and no ionization: 8.7 s/pt/st

• Ionization 2.3 times slower!

• Radiation either 1.9 or 2.2 times slower.

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ConclusionsConclusions

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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