Turbulence simulations with ENZO and FLASH3
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1 Turbulence simulations with ENZO and FLASH3... not yet Adaptive-mesh simulations with FLASH Christoph Federrath Institute for Theoretical Astrophysics Heidelberg Collaborators: Ralf Klessen, Robi Banerjee, Thomas Peters, Wolfram Schmidt, Jens Niemeyer, Markus Hupp, Andreas Maier
2 Outline ENZO vs. FLASH3 in turbulence simulations Turbulence in star formation 2D test case: Kelvin-Helmholtz-instability 3D test case: driven/forced turbulence Conclusions
3 Motivation for turbulence studies Random motion observed in molecular clouds Supersonic compressible turbulence (typical rms Mach numbers are ~1-10) Turbulence as key ingredient in star formation theory (e.g., Mac Low & Klessen 2004; Elmegreen & Scalo 2004, Padoan & Nordlund 2002) Hierarchical structure Lifetime of molecular clouds Orion nebula M42 (HST 2006) Mass distribution (IMF)
4 Code comparison ENZO vs. FLASH3
5 Features of ENZO and FLASH3 for turbulence simulations in star formation: ENZO Parallelized using MPI AMR HDF5 data output PPM (shocks) Particles (passive/active) Self-gravity (Cooling, Heating) FLASH3 Parallelized using MPI AMR HDF5 data output PPM (shocks) Particles (passive/active) Self-gravity (Cooling, Heating) (Magnetic fields)
6 2 dimensional turbulence test case: Kelvin-Helmholtz Helmholtz-instability
7 2D turbulence test case: Kelvin-Helmholtz-instability: 256x128 grid cells (no AMR) Periodic BC in x, outflow BC in y Uniform density Upper half: velocity to the left + sinusoidal velocity perturbation in y Lower half: velocity to the right Isothermal equation of state (gamma = 1.001) units included in setup Physics/hydro/HydroMain/split/PPM/PPMKernel physics/eos/eosmain/gamma Particles/.../passive Grid/.../UG IO/.../hdf5/serial/UG (piecewise parabolic method) (gamma law equation of state) (tracer particles (256x90)) (uniform grid) (HDF5 uniform grid output) Grid/.../Paramesh3/... IO/.../hdf5/serial/PM (paramesh3, but NO AMR) (HDF5 paramesh output)
8 FLASH3 vs. ENZO enstrophy = vorticity 2 = (nabla x v) 2
9 FLASH3 uniform grid (UG) vs. FLASH3 paramesh3 (PM) enstrophy = vorticity 2 = (nabla x v) 2
10 2D turbulence test case: Kelvin-Helmholtz-instability: performance comparison 256x128 grid cells (no AMR) Uniform grid is ~3x faster than paramesh3 and scales slightly better
11 2D turbulence test case: Kelvin-Helmholtz-instability: performance comparison 256x128 grid cells (no AMR) Uniform grid is ~3x faster than paramesh3 and scales slightly better ENZO lies in between FLASH3 UG and FLASH3 PM
12 2D turbulence test case: Kelvin-Helmholtz-instability: performance comparison 256x128 grid cells (no AMR) Uniform grid is ~3x faster than paramesh3 and scales slightly better ENZO lies in between FLASH3 UG and FLASH3 PM Passive particles have minor effect on overall computational cost in both codes
13 3 dimensional turbulence test case: driven/stirred/forced turbulence
14 driven/stirred/forced turbulence
15 3D turbulence test case: driven/stirred/forced compressible turbulence Stochastic forcing term f as source term in equations of hydrodynamics: Physical force field f is constructed and evolved in Fourier space (typically only k=1,2,3 are driven) according to a 3D stochastic Ornstein- Uhlenbeck process with finite autocorrelation time (Eswaran & Pope 1988) f varies smoothly in space and time!
16 3D turbulence test case: driven/stirred/forced compressible turbulence Stochastic forcing term f as source term in equations of hydrodynamics: Decomposition into compressive modes (nabla x f = 0) and solenoidal (nabla f = 0) ENZO supports both compressive and solenoidal forcing, whereas FLASH3 currently only supports solenoidal forcing.
17 3D turbulence test case: driven/stirred/forced compressible turbulence Stochastic forcing term f as source term in equations of hydrodynamics: Decomposition into compressive modes (nabla x f = 0) and solenoidal (nabla f = 0) ENZO supports both compressive and solenoidal forcing, whereas FLASH3 currently only supports solenoidal forcing.
18 3D turbulence test case: driven/stirred/forced compressible turbulence Stochastic forcing term f as source term in equations of hydrodynamics: Decomposition into compressive modes (nabla x f = 0) and solenoidal (nabla f = 0) ENZO supports both compressive and solenoidal forcing, whereas FLASH3 currently only supports solenoidal forcing.
19 3D turbulence test case: driven/stirred/forced compressible turbulence Stochastic forcing term f as source term in equations of hydrodynamics: compressive modes (nabla x f = 0) and solenoidal (nabla f = 0) Stronger shocks / larger voids ( AMR) rather space filling structures Compressive modes excited rather in the interstellar medium (supernovae, gravitational instability, protostellar outflows,... converging flows) Schmidt & Federrath 2007, PRE submitted Federrath, Schmidt, Klessen 2007, ApJ submitted Schmidt, Federrath, Hupp, Maier, Niemeyer 2007, in preparation
20 3 dimensional turbulence test case: driven/stirred/forced turbulence
21 3D turbulence test case: driven/stirred/forced compressible turbulence Resolution: ; uniform grid (no AMR); periodic boundaries; uniform density, gas initially at rest; rms Mach number ~3.5; tracer particles, solenoidal forcing 3 simulations ENZO FLASH3 FLASH3 visc Parabolic Fourier spectrum for force field on k=[1,3] cvisc =0.0 use_steepening =false Peak Fourier spectrum for force field on k=[1,2] cvisc=0.0 use_steepening=false Peak Fourier spectrum for force field on k=[1,2] cvisc=0.1 use_steepening=true Additional modules included: physics/sourceterms/stir/stirmain
22 3D turbulence test case: driven/stirred/forced compressible turbulence Temporal evolution of root mean squared Mach number: T cross = box size / rms velocity
23 3D turbulence test case: driven/stirred/forced compressible turbulence Probability distribution function (PDF) of the density: Log-normaldistribution width of the distr.: (Padoan, Nordlund, Jones 1997)
24 Turbulence Turbulence is random motion (Re>1000) Turbulence develops kinetic energy cascade
25 Turbulence Turbulence is random motion (Re>1000) Turbulence develops kinetic energy cascade
26 Turbulence Turbulence is random motion (Re>1000) Turbulence develops kinetic energy cascade molecular cloud 10pc protostellar cores 0.1pc Protostars pc
27 Turbulence Turbulence is random motion (Re>1000) Turbulence develops kinetic energy cascade E(k) k -2.0 shock-dominated Ma > 1 (e.g., Burgers turbulence) E(k) k -5/3 incompressible Ma < 1 (Kolmogorov 1941)
28 3D turbulence test case: driven/stirred/forced compressible turbulence Energy spectrum functions:
29 3D turbulence test case: driven/stirred/forced compressible turbulence Energy spectrum functions: driven scales
30 3D turbulence test case: driven/stirred/forced compressible turbulence Energy spectrum functions: driven scales nearly inertial subrange
31 3D turbulence test case: driven/stirred/forced compressible turbulence Energy spectrum functions: driven scales nearly inertial subrange dissipation
32 3D turbulence test case: driven/stirred/forced compressible turbulence performance: running on 64 cpus (Intel Itanium) ENZO FLASH3 FLASH3 visc 467 cpu-h 272 cpu-h 243 cpu-h (Uniform Grid mode) (Uniform Grid mode)
33 Conclusions 2D test case: Kelvin-Helmholtz-instability 3D test case: forced compressible turbulence FLASH3 and ENZO both produce robust and statistically similar results FLASH3 Uniform Grid is ~2x faster than ENZO and ~3x faster than FLASH3 Paramesh3 Passive particles have minor effect on overall computatinal cost in both codes Outlook Modify FLASH3 stirring implementation to account for compressive forcing include self-gravity, smart sink particles, magnetic fields, AMR
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