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Pencil Code: multi-purpose and multi-user maintained

Pencil Code: multi-purpose and multi-user maintained

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Pencil Code: multi-purpose and multi-user maintained

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  1. 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)

  2. 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

  3. 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 A=f(:,:,:,iAx:iAz), B=B(nx,3)

  4. 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

  5. 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

  6. (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

  7. Wavenumber characteristics

  8. Higher order – less viscosity

  9. Less viscosity – also in shocks

  10. (ii) High-order temporal schemes Main advantage: low amplitude errors 2N-RK3 scheme (Williamson 1980) 2nd order 3rd order 1st order

  11. Shock tube test

  12. Increase in # of auto tests

  13. Evolution of code size User meetings: 2005 Copenhagen 2006 Copenhagen 2007 Stockholm 2008 Leiden 2009 Heidelberg

  14. Pencil Code check-ins

  15. Vector potential • B=curlA, advantage: divB=0 • J=curlB=curl(curlA) =curl2A • Not a disadvantage: consider Alfven waves B-formulation A-formulation 2nd der once is better than 1st der twice!

  16. Comparison of A and B methods

  17. Faster and bigger machines

  18. 256 processor run at 10243

  19. 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

  20. Online data reduction and visualization non-helically forced turbulence

  21. Scalars on periphery of the box

  22. MRI turbulenceMRI = magnetorotational instability 2563 w/o hypervisc. t = 600 = 20 orbits 5123 w/o hypervisc. Dt = 60 = 2 orbits

  23. Vorticity and Density See poster by Tobi Heinemann on density wave excitation!