1. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Large-Scale Simulation of Ultra-Fast Laser Machining A preliminary outline of a possible proposal to NSF Ananth Grama, CS Jayathi Murthy, ME Ahmed Sameh, CS Xianfan Xu, ME

2. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Outline  Physics of ultra-fast laser machining and review of work done so far (Xu)  Unstructured finite volume methods (Murthy)  Advances in molecular dynamics simulation (Grama)

3. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Unstructured Finite Volume Methods  Arbitrary unstructured convex polyhedra  Conservative cell centered formulation  Equal-order (co-located/non-staggered) storage  Pressure-based method; sequential solutions of pressure and velocity (SIMPLE family)  Algebraic multigrid scheme for linear solution  Non-conformal meshes

4. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Basic Algorithm  Best described for a scalar transport equation  Models diffusive/convective transport of a generic scalar  Most governing equations can be cast into a similar form

5. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging TechnologiesDiscretization  Discretize domain into arbitrary convex polyhedra  triangles, quadrilaterals  tetrahedra, hexahedra,  prisms, pyramids  Independent variables associated with cell and boundary face centroids  Cell shape independent discretization  Non-conformal interfaces permitted  Gradient calculation through reconstruction  Co-located storage of pressure and velocity  Sequential pressure-based solution algorithm

6. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Cell Balance  Integration over the control volume C0 yields  Need to express face fluxes in terms of unknowns at cells  Gradients through reconstruction  Second-order discretization C0 f

7. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Algebraic Multigrid Method  Used for solution of (nominally) linear sparse systems  Create coarse level equations algebraically by adding fine level equations together  Coefficient based agglomeration  optimal performance for each linear set  Can use simple relaxation sweeps  Standard cycling strategies

8. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Natural Convection

9. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Nusselt No. Comparison

10. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Simulation of Sub-micron Heat Transfer Elastic Continuum Lattice Dynamics Boltzmann Transport Equation Fourier Conduction & Variants Silicon 2-3 nmSilicon  ~300 nm Nanotubes Superlattices Thin Films Fully Depleted SOI

11. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Hierarchy of Simulation Electrons & HolesPhonons Increasing Complexity

12. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Sub-Micron Conduction in Bed of Rods 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 k s /(1/3)Cv 2 =0.1 Planck number k s /(v)/(4T 1 3 ) =0.1364 Fourier calculations done for comparison with k i =(1/3)Cv 2

13. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Computational Mesh Stacking 18,592 triangular cells 4x4x1x10 angular discretization Non- conformal interfaces

14. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Comparison with Fourier Conduction As acoustic thickness falls, emission from rods is lost to boundaries, decreasing overall heat transfer

15. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Small Heat Source Effects x y diffuse TwTw L d d x 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

16. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies BTE/Fourier Comparison boundary scattering absentWith diffuse boundary scattering

17. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Coupled Ordinate Method for Non-Gray BTE Unsteady conduction in trapezoidal cavity 4x4x1x10 angular discretization per octant 650 triangular cells Time step =  /100

18. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Challenges for Continuum Simulations  Continuum simulations will remain an important component for analysis in the near future  Extremely large pressure gradients, well beyond those encountered in normal fluid flows – stable algorithms?  Interface tracking & algorithm stability  Are there ways to model phase explosion within continuum context?

19. MEIAC 2001 COMET Laboratory for Computational Methods in Emerging Technologies Coupled Continuum/MD  Will need to mix MD/continuum because MD not affordable on real domain  Solution-adaptive methods for continuum/MD simulations  How to transfer heat/mass/momentum conservatively between regions?  How to avoid spurious reflections at interfaces?  Criteria for automatic switching?  Efficient parallel implementations of very different algorithms in different regions