Filtered Density Function (for LES) and the Potentials for its - PowerPoint PPT Presentation

Filtered Density Function (for LES) and the Potentials for its Quantum Computation Peyman Givi Mechanical Engineering at Pitt Collaborators: S. Levent Yilmaz Center for Simulation and Modeling at Pitt Andrew Daley and Jeremy Levy Physics and Astronomy at Pitt Rolando Somma, LANL Steve Pope, Cornell University Pete Strakey, NETL, DOE Naseem Ansari, Fluent and Pitt Patrick Pisciuneri and Mehdi Nik, Pitt

Outline 1. LES via FDF. 2. Towards Petascale FDF Simualtion. 3. Quantum Speed-up? NIA CFD Conference, Hampton, VA, August 2012

Filtered (Mass) Density Function • PDF at the subgrid scale (SGS). • Scalar-FDF: SGS chemical reaction effects in a closed form. • Velocity-Scalar FDF: SGS convection in a closed form. • More parameters FDF: more complex physics. Q l , , , , Q x t Q x t Q x t G x x dx l L l , , , | , , , , , , , ; x t Q x t Q x t V F V x t dVd d d L l L l NIA CFD Conference, Hampton, VA, August 2012

Low Speed Combustion u j l l L 0 t x j u u , u u u p j i L i j i l L ij l l L L l t x x x x j i j j u , u J j L j l L j l l L L S l t x x x j j j SGS unclosed terms: , , u u u u u u u u u L i j i j i j L j j j L L L L L L S S l l L 4 NIA CFD Conference, Hampton, VA, August 2012

VS-FDF Fine Grain Density: 3 N s , ; , , , , , V u x t x t V u x t x t k k k 1 1 FDF: , , ; , , ; , , , F V x t x t V u x t x t G x x dx L , , ; F V x t dVd L l 5 NIA CFD Conference, Hampton, VA, August 2012

High Speed Turbulence u j l l L 0 t x j u u , u u u p j i L i j i ij l L l l L L l t x x x x j i j j u e , e u e q j L j j l L l l L L t x x x j j j u u i i L L p ij d l x x j i , u u J j L j l L j l l L L t x x x j j j 6 NIA CFD Conference, Hampton, VA, August 2012

EPVS-FDF Fine Grain Density: , , , ; , , , , , , , V u x t x t e x t p x t N 3 s , , , , V u x t x t e x t p x t k k k 1 1 FDF: , , , , ; , , , , ; , , , , , , , F V x t x t V u x t x t e x t p x t G x x dx L , , , , ; F V x t dVd d d L l 7 NIA CFD Conference, Hampton, VA, August 2012

Exact VS-FDF Transport / F V F F L j L L S F L t x x x j j j 2 u 1 p V u j i , , F V F L L V x V V x x i i i j k k u u 1 1 2 j j , , V F V F L L 3 V x x V x x i j i i i j 2 2 u i 2 , , V F V F L L V x x x x i j j j j 8 NIA CFD Conference, Hampton, VA, August 2012

Langevin Descriptor • Lagrangian vector variables , , , , Z t X U E P • Diffusion process , , dZ t D Z t t dt E Z t t dW t • Compare the corresponding Fokker-Planck equation with FDF ... , ... D E 9 NIA CFD Conference, Hampton, VA, August 2012

Fokker-Planck u p u 1 2 1 F V F F F F j i L i L l L L L L L t x x V x x V x x V i i i j j i j i i l l l F L G V u F u 2 1 F ij j j L j L l L L 3 x x V V x x i j i i i i l u 2 2 2 u u 1 F F F j k i L L L C 0 2 x x V x x V V V V i i j j j k i i i l l F e F u 1 C L L L L i e L C F ij L x j 2 2 2 2 2 B F B F 1 AF AF 1 1 1 L L L L 2 2 2 2 2 2 2 2 B F B F 1 1 L L 2 10 NIA CFD Conference, Hampton, VA, August 2012

Modeled 2 nd Order SGS Equations , , , u u u u u u u L i j k L i j L i j l l L , , P u u u ij L k i j l l t x x x k k k , , G u u G u u C jk L k i ik L k j 0 ij l l , , , u L k L L l l L , , P u L k l l t x x x k k k L L 2 2 , C L l x x k k , , u u u , u L i k L i L i l l L , , P u u i L k i l l t x x x k k k , , G u C u ik L k L i l l 11 11 NIA CFD Conference, Hampton, VA, August 2012

FDF Simulation Typically Lagrangian Monte Carlo elements on Eulerian grids.  Complex domain.  10**9 grids /elements.  10**11 MC particles.  Mostly reduced kinetics. NIA CFD Conference, Hampton, VA, August 2012

Example 1: Sydney-Sandia Swirl Burner NIA CFD Conference, Hampton, VA, August 2012

FDF vs. RANS: Axial Velocity LES / FDF RANS Z = 20 mm Z = 40 mm NIA CFD Conference, Hampton, VA, August 2012

FDF vs. RANS : Temperature LES / FDF RANS Z = 20 mm Z = 40 mm NIA CFD Conference, Hampton, VA, August 2012

FDF vs. RANS: CO2 Mass Fraction LES / FDF RANS Z = 20 mm Z = 40 mm NIA CFD Conference, Hampton, VA, August 2012

Example 2: DLR PRECCINSTA Burner Reasonable representation of an industrial type gas turbine combustor. Combustor features a plenum, a swirler & a square combustion chamber. CH 4 fuel at equivalence ratio of 0.83 fed through 12 injection holes within the radial swirler. Dry air at ambient temperature fed via the plenum through the radial swirlers. Total mass flow rate = 12.9 g/s Combustion chamber cross section = 85 mm x 85 mm Combustion chamber height = 114 mm NIA CFD Conference, Hampton, VA, August 2012

DLR Flame NIA CFD Conference, Hampton, VA, August 2012

DLR Flame MEAN CO 2 MEAN Temperature RMS CO 2 NIA CFD Conference, Hampton, VA, August 2012

Towards Petascale FDF Simulation Typically the domain is regularly portioned Inefficient on massively parallel platform 20 NIA CFD Conference, Hampton, VA, August 2012

Irregularly Portioned Processors Partition in to subdomains Connectivity between subdomains: Local data Neighboring data Communication patterns Data structures 1D arrays that map to a global 3D array Particle lists Array of particle lists (bins) NIA CFD Conference, Hampton, VA, August 2012

NIA CFD Conference, Hampton, VA, August 2012

Scalability NIA CFD Conference, Hampton, VA, August 2012 NICS/Kraken

Example: Bunsen Burner NIA CFD Conference, Hampton, VA, August 2012

Quantum Computing • Quantum computers use special properties of microscopic objects to process information • Information in a classical computer is stored as bits • In a quantum computer it is stored as qubits A qubit can be in a superposition of 0 and 1 NIA CFD Conference, Hampton, VA, August 2012

Example 1: 38468522360287713067145227649177955801213487701099 • Perform certain tasks 89956280167263288492906413250106234738923625487248 much faster than a normal 43632748829239471099553846946567828308577705718806 94978568779355941701709253073909647758709792262685 (classical) computer 32784959698795712324287283270444145525795129254121 120710346037881026114574883283576878022850732431110 88058576663938238037682029535630748718401810408271 7619027814399839319656394117300027235594739384321 • e.g., quantum computers = can factor numbers 19151078601511813582801009133095143365412697691872 exponentially faster than 82849826678249401200032709416910316550320010920704 classical computers (Shor, 37797665474841228343134658535223112172218027305038 1994) 34496265576199132087913176183816562977572021862399 X 20086869862907331390554301660726422765403303838159 28513728233298852507348154165945582548188931037072 Difficulty of factoring 13279188964772171854249281063180682234029182739436 25886101798462506273138523315831932882407840022527 numbers is foundation 9 of public key encryption NIA CFD Conference, Hampton, VA, August 2012

Example 2: DATABASE SEARCH (Grover) Telephone book with N =1,000,000 entries Task: find name of person whose number is: (757) 864-6228 Ordinary Phonebook Quantum Phonebook Number found after Number found after ~N 1/2 =1000 attempts ~N/2=500,000 attempts • Other algorithms with quantum speed-ups for: sparse linear equations, classical simulated annealing, quantum Monte- Carlo computations,… NIA CFD Conference, Hampton, VA, August 2012

Power of Quantum Computers • They can represent many outcomes at once • Single qubit: 2D space • Many qubits: 2 n complex numbers describe the state A state with n=1000 qubits is specified by 2 1000 ~10 300 coefficients ! NIA CFD Conference, Hampton, VA, August 2012

Operation NIA CFD Conference, Hampton, VA, August 2012

General Structure: Classical S Step 1: Initialize (boot) computer. 1 (0) 1 S 0 n 1 2 2 1 S 1 Step 2: Gate operations S F S 0 1 2 n 2 1 1 Step 3: Read out answer a ( ) 1 F S a a 0 1 2 n 2 1 NIA CFD Conference, Hampton, VA, August 2012

General Structure: Quantum Step 1: Initialize quantum computer. 1 0 0 n 0 1 2 2 1 Step 2: Quantum gate operations 1 1 1 ˆ i H t t n n n 0 0 0 1 1 1 2 2 2 2 2 2 1 1 1 Step 3: Quantum measurement 1 1 2 P a a n n 0 0 1 1 2 2 2 2 1 1 a a NIA CFD Conference, Hampton, VA, August 2012

Hardware Many implementations are being explored, with components already demonstrated: • Neutral atoms • Trapped ions • Color centers (e.g., NV-centers in diamond) • Quantum dots • Superconducting qubits (charge, phase, flux) • Nuclear Magnetic Resonance systems • Optical qubits State of the art • 14 entangled qubits with several hundred gate operations – trapped ions • Large qubit arrays (ca. 500) with neutral atoms (but slow gate timescales) • Fast gate operations demonstrated with superconducting qubits NIA CFD Conference, Hampton, VA, August 2012