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Modern Particle Methods for Complex Flows G. Amati (2), F. Castiglione (1), F. Massaioli(2), S. Succi (1) Acks to:

Modern Particle Methods for Complex Flows G. Amati (2), F. Castiglione (1), F. Massaioli(2), S. Succi (1) Acks to: G. Bella (Roma), M. Bernaschi(IAC), H. Chen (EXA), S. Orszag (Yale), E. Kaxiras (Harvard), S. Ubertini (Roma). Istituto Applicazioni del Calcolo

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Modern Particle Methods for Complex Flows G. Amati (2), F. Castiglione (1), F. Massaioli(2), S. Succi (1) Acks to:

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  1. Modern Particle Methods for Complex Flows G. Amati (2), F. Castiglione (1), F. Massaioli(2), S. Succi (1) Acks to: G. Bella (Roma), M. Bernaschi(IAC), H. Chen (EXA), S. Orszag (Yale), E. Kaxiras (Harvard), S. Ubertini (Roma) • Istituto Applicazioni del Calcolo • Mauro Picone , CNR, Roma, Italy • 2) CASPUR, Roma, Italy

  2. Why Particle Methods? Atomistic physics PDEs with large distorsions (Astrophysics) Moving geometries (Combustion) Moving interfaces (Multiphase flows)

  3. Classical Particle Methods • Particle-Particle (Molecular dynamics, Monte Carlo) • Particle-Mesh (Neutral Plasmas, Semiconductors) • P3M (Gravitational,Charged Plasmas) • Fluids? • J.Eastwood, R. Hockney: Computer Simulations using particles

  4. Particle Methods: pros and cons • Pros: • Geoflexibility (boundary conditions) • Physically Sound • No matrix algebra • Cons: • Noisy • Small timesteps

  5. New Particle Methods for Fluid Flows Simple fluids, complex flows: The Navier-Stokes equations are very hard to solve: Complex fluids, complex flows: Fluid equations are often NOT KNOWN!

  6. Fluids (3D) Kinetic Theory (6D) Phase – space Fluid (6N D) Atoms / Molecules New Particle Methods for Fluid Flows • Idea: Solve fluid equations using fictitious quasi-particle dynamics • Universality: Molecular details do NOT count • Driver: Statistical Physics (front-end) , Numerical Analysis (back-end) • Lattice Gas Cellular Automata (LGCA) • Lattice Boltzmann (LBE) • Dissipative Particle Dynamics (DPD)

  7. Details dont count: quasi-particle trajectories Coarse-Graining via 'Superparticles': B blocking factor: (Macro to Meso to Micro scale) 1 computational particle = B molecules

  8. Coarse-grained equations Modeling goes into FIJ

  9. Free stream Collision Details dont count: kinetic theory Pre-averaged distributions: Boltzmann approach (Probabilistic) Modeling goes into f and C(f,f)

  10. 3 2 1 4 5 6 001001 Lattice Gas Cellular Automata Boolean representation: n_i=0,1 particle absence/presence

  11. t+1 t+1+ε t 2 3 4 1 i 5 6 streaming collision Lattice Gas Cellular Automata 0absence ni = i = 0,61 presence collisions (Frisch, Hasslacher, Pomeau, 1986)

  12. Boundary condition

  13. From LGCA to Navier-Stokes Conservation laws: (mass) (momentum) (energy) No details of molecular interactions (true collision) (lattice collision)

  14. From LGCA to Navier-Stokes Isotropy (Rotational invariance) such that:

  15. Von Karman street

  16. LGCA: blue-sky scenario • Exact computing (Round-off freedom) • Ideal for parallel computing (Local) • Flexible boundary conditions • LGCA: grey-sky scenario • Noise (Lots of automata) • Low Reynolds (too few collisions) • Exponential complexity 2^b (3D requires b=24) • Lack of Galilean invariance

  17. From LGCA to (Lattice) Boltzmann • (Boolean) molecules to (discrete) distributions ni fi = < ni > • (Lattice) Boltzmann equations (LBE)

  18. From (Lattice) Boltzmann to Navier - Stokes M(density) M(speed) E(temperature) P (pressure tensor)

  19. From (Lattice) Boltzmann to Navier - Stokes Weak Departure from local equilibrium

  20. From (Lattice) Boltzmann to Navier - Stokes M M LBE E

  21. THE LBE STORY • Non-linear LBE (Mc Namara-Zanetti, 1988), noise-free • Quasi-linear LBE (Higuera-Jimenez, 1989), 3D sim’s • EnhancedLBE (Higuera-Succi-Benzi, 1989), High Reynolds, TOP-DOWN approach • G-invariant LBE (Chen-Chen-Mattheus, 1991), Galilean invariant

  22. LATTICE BGK Since Re depends only on , single time relaxation only Viscosity (lattice sound speed) Qian, d’Humières, Lallemand, 1992

  23. LBE assets: Noise-free, high Reynolds Flexible Boundary Conditions Efficient on serial, even more on parallel Poisson-freedom Additional physics (beyond fluids) Quick grid set up (EXA-Powerflow) LBE liabilities Later … Who needs LBE? DON’T USE: Strong heat transfer, compressibility (combustion) CAN USE: Turbulence in simple geos SHOULD USE: Porous media MUST USE: Multiphase, Colloidal, External Aerodynamics

  24. Parallel Speed-up Amati, Massaioli, Bernaschi, Scicomp 2002

  25. LBE t=5000 t=20000 t=0 SP Ansumali et al, ETHZ+IAC

  26. Turbulent channel APE-100: 10 Gflops sustained (Amati , Benzi, Piva, Succi, PRL 99)

  27. Porous media: random fiber networks A.Hoekstra,P Sloot, A.Koponen, J Timonen, PRL 2001

  28. Cristal Growth Miller, Succi, Mansutti, PRL 1999

  29. LBE-Multiphase, Demixing flow: Amati, Gonnella, Lamura, Massaioli

  30. LBE: Multiphase B. Palmer, D. Rector, pnl.gov http://gallery.pnl.gov/mscf/bubble_web1/bubble_web.mpg

  31. Local grid refinement Different time scales and no. of time steps for different refinement levels, interpolation between levels Succi, Filippova, Smith, Kaxiras 2001,

  32. LBE: Airfoils Succi,Filippova,Kaxiras, Cise 2001

  33. You can do something like this… Bella, Ubertini, 2001

  34. Powerflow, EXA LBE: Car design H Chen, S Kandasamy, R Shock, S. Orszag, S. Succi, V. Yakhot, Science (2003)

  35. LBE: Reactive microflows

  36. LBE: Multiscale microflows

  37. Unstructured LBE Ubertini,Succi,Bella, 2003

  38. Unstructured LBE

  39. LBE: Unstructured (soon moving) grids

  40. Lattice Boltzmann: Future Agenda * Better (non-linear) stability * Turbomodels (boundary conditions) * Thermal consistency, Potential energy * High-Knudsen (challenge true Boltzmann?) * Moving grids * Multiscale coupling

  41. Dissipative particle dynamics LGCA: too stiff MD: Too expensive LBE: Grid-Bound http://www.bfrl.nist.gov/861/vcttl/talks/talkG/sdl001.html

  42. Pressure: Viscosity: DPD thermodynamics

  43. DPD applications • Colloidal suspensions • Dilute polymers • Phase separation • Model membranes

  44. DPD: High-density suspension under shear http://www.bfrl.nist.gov/861/vcttl/talks/talkG/sdl001.html

  45. Phase separation Prof Coveney’s group

  46. DPD: Amphiphiles http://www.lce.hut.fi/research/polymer/dpd.shtml

  47. DPD: pros and cons • + Thermodynamically consistent • + Flexible (Grid-free) • + Soft forces allow large dt • Adaptive versions (Voronoi) are complex • - Theory still in flux (?)

  48. Conclusions and Future Prospects • Strengths: • Much faster than MD • Comparable with grid methods • Highly flexible • Amenability to parallel computing • Future: • Multiscale hybrids • Grid computing

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