Pencil Code: multi-purpose and multi-user maintained

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Pencil Code multi-purpose and multi-user
maintained

• Axel Brandenburg (Nordita, Stockholm)
• Wolfgang Dobler (Univ. Calgary)
• and now many more.

(...just google for Pencil Code)
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PencilCode

• Started in Sept. 2001 with Wolfgang Dobler
• High order (6th order in space, 3rd order in
  time)
• Cache memory efficient
• MPI, can run PacxMPI (across countries!)
• Maintained/developed by 40 people (SVN)
• Automatic validation (over night or any time)
• Max resolution so far 10243 , 4096 procs

• Isotropic turbulence
• MHD, passive scl, CR
• Stratified layers
• Convection, radiation
• Shearing box
• MRI, dust, interstellar
• Self-gravity
• Sphere embedded in box
• Fully convective stars
• geodynamo
• Other applications
• Homochirality
• Spherical coordinates

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Pencil formulation

• In CRAY days worked with full chunks
  f(nx,ny,nz,nvar)
• Now, on SGI, nearly 100 cache misses
• Instead work with f(nx,nvar), i.e. one nx-pencil
• No cache misses, negligible work space, just 2N
• Can keep all components of derivative tensors
• Communication before sub-timestep
• Then evaluate all derivatives, e.g. call
  curl(f,iA,B)
• Vector potential Af(,,,iAxiAz), BB(nx,3)

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Switch modules

• magnetic or nomagnetic (e.g. just hydro)
• hydro or nohydro (e.g. kinematic dynamo)
• density or nodensity (burgulence)
• entropy or noentropy (e.g. isothermal)
• radiation or noradiation (solar convection,
  discs)
• dustvelocity or nodustvelocity (planetesimals)
• Coagulation, reaction equations
• Chemistry (reaction-diffusion-advection equations)

Other physics modules MHD, radiation, partial
ionization, chemical reactions, selfgravity
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High-order schemes

• Alternative to spectral or compact schemes
• Efficiently parallelized, no transpose necessary
• No restriction on boundary conditions
• Curvilinear coordinates possible (except for
  singularities)
• 6th order central differences in space
• Non-conservative scheme
• Allows use of logarithmic density and entropy
• Copes well with strong stratification and
  temperature contrasts

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(i) High-order spatial schemes
Main advantage low phase errors
Near boundaries
x x x x x x x x x
ghost zones
interior points
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Wavenumber characteristics
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Higher order less viscosity
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Less viscosity also in shocks
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(ii) High-order temporal schemes
Main advantage low amplitude errors
2N-RK3 scheme (Williamson 1980)
2nd order
3rd order
1st order
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Shock tube test
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Increase in of auto tests
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Evolution of code size
User meetings 2005 Copenhagen 2006
Copenhagen 2007 Stockholm 2008 Leiden 2009
Heidelberg
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Pencil Code check-ins
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Vector potential

• BcurlA, advantage divB0
• JcurlBcurl(curlA) curl2A
• Not a disadvantage consider Alfven waves

B-formulation
A-formulation
2nd der once is better than 1st der twice!
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Comparison of A and B methods
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Faster and bigger machines
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256 processor run at 10243
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Hyperviscous, Smagorinsky, normal
height of bottleneck increased
Haugen Brandenburg (PRE, astro-ph/0402301)
onset of bottleneck at same position
Inertial range unaffected by artificial diffusion
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Online data reduction and visualization
non-helically forced turbulence
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Scalars on periphery of the box
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MRI turbulenceMRI magnetorotational instability
2563 w/o hypervisc. t 600 20 orbits
5123 w/o hypervisc. Dt 60 2 orbits
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Vorticity and Density
See poster by Tobi Heinemann on density wave
excitation!