MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Large-Scale Simulation of Ultra-Fast Laser Machining A preliminary outline

MEIAC 2001 COMETLaboratory for Computational Methods in Emerging Technologies

Large-Scale Simulation of Large-Scale Simulation of Ultra-Fast Laser Machining Ultra-Fast Laser Machining

A preliminary outline of a possible proposal to A preliminary outline of a possible proposal to NSFNSF

Ananth Grama, CSAnanth Grama, CS

Jayathi Murthy, MEJayathi Murthy, ME

Ahmed Sameh, CSAhmed Sameh, CS

Xianfan Xu, MEXianfan Xu, ME


OutlineOutline

Physics of ultra-fast laser Physics of ultra-fast laser machining and review of work machining and review of work done so far (Xu) done so far (Xu)

Unstructured finite volume Unstructured finite volume methods (Murthy)methods (Murthy)

Advances in molecular dynamics Advances in molecular dynamics simulation (Grama)simulation (Grama)


Unstructured Finite Volume Unstructured Finite Volume

MethodsMethods Arbitrary unstructured convex polyhedraArbitrary unstructured convex polyhedra

Conservative cell centered formulationConservative cell centered formulation

Equal-order (co-located/non-staggered) Equal-order (co-located/non-staggered) storagestorage

Pressure-based method; sequential Pressure-based method; sequential solutions of pressure and velocity (SIMPLE solutions of pressure and velocity (SIMPLE family)family)

Algebraic multigrid scheme for linear Algebraic multigrid scheme for linear solutionsolution

Non-conformal meshesNon-conformal meshes


Basic AlgorithmBasic Algorithm Best described for a scalar transport equationBest described for a scalar transport equation

Models diffusive/convective transport of a generic Models diffusive/convective transport of a generic scalarscalar

Most governing equations can be cast into a Most governing equations can be cast into a similar formsimilar form


DiscretizationDiscretization Discretize domain into arbitrary convex polyhedraDiscretize domain into arbitrary convex polyhedra

triangles, quadrilateralstriangles, quadrilaterals

tetrahedra, hexahedra, tetrahedra, hexahedra,

prisms, pyramidsprisms, pyramids

Independent variables associated with cell and Independent variables associated with cell and boundary face centroidsboundary face centroids

Cell shape independent discretizationCell shape independent discretization

Non-conformal interfaces permittedNon-conformal interfaces permitted

Gradient calculation through reconstructionGradient calculation through reconstruction

Co-located storage of pressure and velocityCo-located storage of pressure and velocity

Sequential pressure-based solution algorithmSequential pressure-based solution algorithm


Cell BalanceCell Balance Integration over the control volume C0 Integration over the control volume C0

yieldsyields

Need to express face fluxes in terms of Need to express face fluxes in terms of unknowns at cells unknowns at cells

Gradients through reconstructionGradients through reconstruction

Second-order discretizationSecond-order discretization

C0f


Algebraic Multigrid Method Algebraic Multigrid Method

Used for solution of (nominally) linear sparse systemsUsed for solution of (nominally) linear sparse systems

Create coarse level equations algebraically by adding fine Create coarse level equations algebraically by adding fine level equations togetherlevel equations together

Coefficient based agglomerationCoefficient based agglomeration optimal performance for each linear setoptimal performance for each linear set

Can use simple relaxation sweepsCan use simple relaxation sweeps

Standard cycling strategiesStandard cycling strategies


Natural ConvectionNatural Convection


Nusselt No. ComparisonNusselt No. Comparison


Simulation of Sub-micron Heat TransferSimulation of Sub-micron Heat Transfer

Elastic ContinuumLattice Dynamics

Boltzmann Transport Equation

Fourier Conduction & Variants

Silicon 2-3 nm Silicon ~300 nm

NanotubesSuperlattices

Thin Films

Fully Depleted SOI

SOI


Hierarchy of SimulationHierarchy of Simulation

Schrodinger’sEquation

Monte Carlo

BTE

BTE Moments

Drift Diffusion

ElasticContinuum/Lattice Eqns.

Monte Carlo

BTE

HyperbolicHeatConduction

FourierDiffusion

Electrons & Holes Phonons

Increasing

Complexity


Sub-Micron Conduction in Bed of Sub-Micron Conduction in Bed of RodsRods

• Array of four rows of rods displaced randomly; d/L=5.33

• Rod acoustic thickness » 1=> Fourier conduction in rods

•Interstitial space is acoustically thin=> BTE

•Rods are fully absorbing and emit diffusely; gray

•Emissive power ratio of boundaries =1.013

• ks /(1/3)Cv2 =0.1

•Planck number ks/(v)/(4T13) =0.1364

•Fourier calculations done for comparison with ki =(1/3)Cv2


Computational MeshComputational Mesh

Stacking

18,592 triangular cells

4x4x1x10 angular discretization

Non-conformal interfaces


Comparison with Fourier Comparison with Fourier ConductionConduction

• As acoustic thickness falls, emission from rods is lost to boundaries, decreasing overall heat transfer


Small Heat Source EffectsSmall Heat Source Effects

x

ydiffuse

Tw

L

d

dx

y

z

Unsteady “top hat” function for heat source

Heat source dimension d/L <<1

Variety of small-scale effects

Boundary scattering

Lack of equilibrium between phonon and source because of small size of source

Phonon traverse time also interacts with hot spot on-time


BTE/Fourier ComparisonBTE/Fourier Comparison

boundary scattering absent

x (x/L)

=

(T

BT

E-

TF

ou

r)/(q

L/(

4v

Tw3))

0 0.25 0.5 0.75 1-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

t =0.1t =1.0t =2.0t =5.0

100X10, 8X8, tq =1.0, t =0.001L=5.58

With diffuse boundary scattering

x (x/L)

=

(T

BT

E-

TF

ou

r)/(q

L/(

4v

Tw3))

0 0.25 0.5 0.75 1-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

t =0.1t =1.0t =2.0t =5.0

100X10, 8X8, tq =1.0, t =0.001L=5.58, 1 -D problem


Coupled Ordinate Method for Non-Gray Coupled Ordinate Method for Non-Gray BTEBTE

Sequential COMETAcoustic ThicknessCPU secs Iters CPU secs Iters

2 Bands0.0484 98.68 5 79.52 50.484 98.85 5 69.62 54.84 97.72 6 68.54 548.4 162.25 10 67.95 5484.0 529.4 33 61.22 5

10 Bands0.0484 484.02 6 424.36 60.484 476.23 6 338.19 54.84 772.17 9 338.38 548.4 2922.16 29 337.03 5484.0 19,006.7 191 354.74 5

20 Bands0.0484 970.04 6 958.01 60.484 960.8 6 882.56 64.84 1609.13 10 754.18 548.4 5701.64 34 828.82 6484.0 39,333.2 225 921.48 6

•Unsteady conduction in trapezoidal cavity

•4x4x1x10 angular discretization per octant

•650 triangular cells

•Time step = /100


Challenges for Continuum Challenges for Continuum SimulationsSimulations

Continuum simulations will remain an Continuum simulations will remain an important component for analysis in the important component for analysis in the near futurenear future

Extremely large pressure gradients, well Extremely large pressure gradients, well beyond those encountered in normal fluid beyond those encountered in normal fluid flows – stable algorithms?flows – stable algorithms?

Interface tracking & algorithm stabilityInterface tracking & algorithm stability Are there ways to model phase explosion Are there ways to model phase explosion

within continuum context?within continuum context?


Coupled Continuum/MDCoupled Continuum/MD

Will need to mix MD/continuum Will need to mix MD/continuum because MD not affordable on because MD not affordable on real domain real domain

Solution-adaptive methods for Solution-adaptive methods for continuum/MD simulationscontinuum/MD simulations

How to transfer How to transfer heat/mass/momentum heat/mass/momentum conservatively between regions?conservatively between regions?

How to avoid spurious reflections How to avoid spurious reflections at interfaces?at interfaces?

Criteria for automatic switching?Criteria for automatic switching? Efficient parallel Efficient parallel

implementations of very implementations of very different algorithms in different different algorithms in different regionsregions

MD 2-Temp 1-Temp

Documents

MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Large-Scale Simulation of Ultra-Fast Laser Machining A preliminary outline