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

NIA CFD Conference, Hampton, VA, August 2012

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.

, , , | , , , , , , , ;

L l L l

x t Q x t Q x t V F V x t dVd d d

, , ,

l

Q x t Q x t G x x dx

,

l L l

Q Q x t

NIA CFD Conference, Hampton, VA, August 2012

Low Speed Combustion

4 j l l L j

u t x

,

j i i ij l L l l L l L j i L i j j j

u u u p t x x x u u x ,

j j l L l l L j j j L j l L

u J u t x x S x

SGS unclosed terms:

,

L i j i j i j L L L

u u u u u u ,

L j j j L L L

u u u

l l L

S S

NIA CFD Conference, Hampton, VA, August 2012

VS-FDF

5

Fine Grain Density:

3 1 1

, ; , , , , ,

s

N k k k

V u x t x t V u x t x t

, , ; , , ; , , ,

L

F V x t x t V u x t x t G x x dx

, , ;

L l

F V x t dVd

FDF:

NIA CFD Conference, Hampton, VA, August 2012

High Speed Turbulence

6 j l l L j

u t x ,

j i i ij l L l l L l L j i L i j j j

u u u p t x x x u u x ,

L j j l L l l L L j j j i i L L ij l j j d i

u e e q t x x x u u p x x e u ,

j j l L l l L L j j j j L

u J t x u x x

NIA CFD Conference, Hampton, VA, August 2012

EPVS-FDF

7

Fine Grain Density:

3 1 1

, , , ; , , , , , , , , , , ,

s

N k k k

V u x t x t e x t p x t V u x t x t e x t p x t

, , , , ; , , , , ; , , , , , , ,

L

F V x t x t V u x t x t e x t p x t G x x dx

, , , , ;

L l

F V x t dVd d d

FDF:

NIA CFD Conference, Hampton, VA, August 2012

Exact VS-FDF Transport

8 2 2

/ 1 , , 1 1 2 , , 3 2

L L j j j i L L j L L j i i i j k k j j L L i j i i i j i

F F t x x u u p V F V F V x V V x x u u V F V F V x x V x F x V S F x V

2

, ,

i L L j j j j

u V F V F x x x x

NIA CFD Conference, Hampton, VA, August 2012

Langevin Descriptor

9

• Lagrangian vector variables
• Diffusion process
• Compare the corresponding Fokker-Planck equation with FDF

, , , , Z t X U E P , , dZ t D Z t t dt E Z t t dW t

... , ... D E

NIA CFD Conference, Hampton, VA, August 2012

Fokker-Planck

10

1 2 1 2 1 3

j i i L l L L L L L L i i i j j i j i i l l l L ij j j L j L l L L i j i i i i l

u p u V F F F F F t x x V x x V x x V F G V u F u F x x V V x x

2 2

2 1 2 1 1

j k i L L L i i j j j k i i i l l L L L L i e L ij L j L

u u u F F F C x x V x x V V V V F e F u C C F x AF

2 2 2 2 2 2 2 2 2 2 2 2

1 1 1 2 1 1 2

L L L L L

B F B F AF B F B F

NIA CFD Conference, Hampton, VA, August 2012

Modeled 2nd Order SGS Equations

11 11

, , , , , , ,

L i j k L i j L i j l l L ij L k i j l l k k k jk L k i ik L k j ij l l

u u u u u u u P u u u t x x x G u u G u u C

, , , , , 2 2 ,

L k L L l l L L k l l k k k L L L l k k

u P u t x x x C x x , , , , , , ,

L i k L i L i l l L i L k i l l k k k ik L k L i l l

u u u u P u u t x x x G u C u

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

Z = 20 mm Z = 40 mm LES / FDF RANS

NIA CFD Conference, Hampton, VA, August 2012

FDF vs. RANS : Temperature

Z = 40 mm Z = 20 mm LES / FDF RANS

NIA CFD Conference, Hampton, VA, August 2012

FDF vs. RANS: CO2 Mass Fraction

Z = 40 mm Z = 20 mm LES / FDF RANS

NIA CFD Conference, Hampton, VA, August 2012

Reasonable representation of an industrial type gas turbine combustor. Combustor features a plenum, a swirler & a square combustion chamber. CH4 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

Example 2: DLR PRECCINSTA Burner

NIA CFD Conference, Hampton, VA, August 2012

DLR Flame

NIA CFD Conference, Hampton, VA, August 2012

DLR Flame

MEAN CO2 MEAN Temperature RMS CO2

NIA CFD Conference, Hampton, VA, August 2012

Towards Petascale FDF Simulation

20

Typically the domain is regularly portioned Inefficient on massively parallel platform

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

NICS/Kraken

NIA CFD Conference, Hampton, VA, August 2012

Example: Bunsen Burner

NIA CFD Conference, Hampton, VA, August 2012

• Quantum computers use special properties of microscopic
• bjects 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

Quantum Computing

NIA CFD Conference, Hampton, VA, August 2012

38468522360287713067145227649177955801213487701099 89956280167263288492906413250106234738923625487248 43632748829239471099553846946567828308577705718806 94978568779355941701709253073909647758709792262685 32784959698795712324287283270444145525795129254121 120710346037881026114574883283576878022850732431110 88058576663938238037682029535630748718401810408271 7619027814399839319656394117300027235594739384321

=

19151078601511813582801009133095143365412697691872 82849826678249401200032709416910316550320010920704 37797665474841228343134658535223112172218027305038 34496265576199132087913176183816562977572021862399

X

20086869862907331390554301660726422765403303838159 28513728233298852507348154165945582548188931037072 13279188964772171854249281063180682234029182739436 25886101798462506273138523315831932882407840022527 9

• Perform certain tasks

much faster than a normal (classical) computer

• e.g., quantum computers

can factor numbers exponentially faster than classical computers (Shor, 1994)

Difficulty of factoring numbers is foundation

• f public key encryption

Example 1:

NIA CFD Conference, Hampton, VA, August 2012

DATABASE SEARCH (Grover) Telephone book with N=1,000,000 entries

Task: find name of person whose number is: (757) 864-6228

Ordinary Phonebook

Number found after ~N/2=500,000 attempts

Quantum Phonebook

Number found after ~N1/2 =1000 attempts

Example 2:

• 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: 2n complex numbers describe the state

A state with n=1000 qubits is specified by 21000 ~10300 coefficients !

NIA CFD Conference, Hampton, VA, August 2012

Operation

NIA CFD Conference, Hampton, VA, August 2012

S

1 2 2 1

n

1 Step 1: Initialize (boot) computer.

(0) 1 S

Step 2: Gate operations

S

1 2 2 1

n

1 Step 3: Read out answer a ( ) 1 F S a

1 2 2 1

n

1

a

S F S

General Structure: Classical

NIA CFD Conference, Hampton, VA, August 2012

1 2 2 1

n

1 Step 1: Initialize quantum computer.

1 2 2 1

n

1

1 2 2 1

n

1

1 2 2 1

n

1 Step 2: Quantum gate operations

ˆ i H t t

1 2 2 1

n

1

a 1 2 2 1

n

1

a

Step 3: Quantum measurement

2

P a a

General Structure: Quantum

NIA CFD Conference, Hampton, VA, August 2012

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

Hardware

NIA CFD Conference, Hampton, VA, August 2012

Realization on a quantum computer SDEs Quantum algorithm

Quantum Speedup for FDF?

NIA CFD Conference, Hampton, VA, August 2012

Summary of FDF Properties

• Turbulence-Chemistry interactions in closed form.
• SGS scalar fluxes in closed form.
• Equivalent to 2nd order closures (at least).
• Quantum computing may be very effective for FDF simulation.
• Applicable to premixed, non-premixed, and partially premixed

flames.

• Applicable to both flamelet and distributed flame regions.
• Continues to gain popularity in turbulence simulation.

NIA CFD Conference, Hampton, VA, August 2012

Popularity of FDF

• UC Berkeley
• Stanford
• Purdue
• Iowa State
• Cornell
• UT Austin
• SUNY-Buffalo
• U. Wyoming
• Michigan State
• CTR/NASA Ames
• NASA Langley
• Sandia Labs
• Rolls Royce
• ANSYS
• .
• .
• .
• England
• France
• Germany
• Netherland
• Portugal
• Russia
• Spain
• Kazakhstan
• Canada
• China
• .
• .
• in FLUENT
• In US3D
• In VULCAN .