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281–283 Accurac INDEX AAE, see Auxiliary algebraic evaluations for manufacturing processes modeling, 739 Absorbing boundaries, 260, 267 overrelaxation with, 68 Absorbing media (Monte Carlo methods), 281–283 for structured meshes, 33 Accuracy: for two and three dimensions, 82–83 of discretization, 926–929 AMBER force field, 666 of numerical solution procedures, 17 AMG method, see Algebraic multigrid method Acoustic mismatch model (AMM), 646, 649 AMM, see Acoustic mismatch model Adaptive grids, 483–489 Amorphous silicon, crystallization of, 680 coarsening, 486 AMR, see Adaptive mesh refinement data compression and mining, 487 AMRC, see Adaptive mesh-refinement and hybrid, 487–488 mesh-coarsening moving boundary problems, 486–487 Anderson method, 670 parallel extensions, 488–489 Anisotropic grids, 480–481 Adaptive mesh refinement (AMR), 484–485, Anisotropic scattering, Monte Carlo 488–490 application to, 285 Adaptive mesh-refinement and mesh-coarsening ANN, see Artificial neural networks (AMRC), 486, 488 Annealing, thermal process for, 748 Added-dissipation schemes, 41, 42 Adiabatic (zero normal derivative) boundary Anomalous diffusion, 631–632, 639–641 conditions, 78 A posteriori series convergence acceleration ADI technique, see Alternating direction implicit schemes, 500 technique Apparent rate of convergence, 423, 424 Adjoint forms of equations, 932 Approximate factoring, 83 Adjoint method: Area coordinates, 103 sensitivity analysis, 458–460 Artificial compressibility methods: stochastic inverse problems, 534–535 for continuity and momentum equations, 43 Algebraic multigrid (AMG) method, 36–37 for incompressible flow, 85 All-speed pressure-based algorithms, 383–341 Artificial neural networks (ANN), 802–804 Alternating direction explicit schemes, 76 Artificial supertriangle approach, 477–478 Alternating direction implicit (ADI) technique: Artificial viscosity, 28 946 INDEX 947 Astronomy, high-performance computing Block iterative methods, 66–67 for, 900 Block-structured meshes (grids), 8, 9, 476 Autohesion (thermoplastics), 792 Blood and blood vessels, see Bioheat transfer Auxiliary algebraic evaluations (AAE), 433–435 Blood perfusion rate, 855 Axisymmetric contraction, 704 Body-fitted meshes, 8 Axisymmetric expansion, 704 for irregular geometry, 314 velocity storage for, 41 Backdiffusion, 610–613 Boltzmann transport equation (BTE), 672, 936 Backward-facing step flow, DNS of, 713–716 Boundary conditions: Backward-implicit-Galerkin method, 114 absorbing, 260 Bayesian approach (inverse heat conduction), adiabatic (zero normal derivative), 78 542–553 appropriate, 56 with Gibbs sampler, 546–547 convective, 79 inverse problem transformation in, 544–546 for direct problems, 525–526 numerical results with, 548–553 finite-difference methods, 55–56 and stochastic inverse heat-conduction problem, finite-element methods, 96–97 542–544 of the first kind, 55 work using, 553 floating random walk, 267–268 Beam-warming scheme, 30 flux, 78–79 BEM, see Boundary-element method high-performance computing, 912–913 Beowulf computer, 898 manufacturing processes modeling, 738, Bernoulli distribution, 294 740–741 Bernoulli trials, 294 molecular dynamics method, 669–670 Biased Monte Carlo methods, 276, 278–281, 294. in Monte Carlo method, 260 See also Importance sampling moving, see Moving-boundary problems BI-CGSTAB, 38 with multigrid method, 71–72 Biconjugate gradients, 38 partially absorbing, 260 BIE (boundary integral equation), 128 pressure-based algorithms, 343–348 BIEM (boundary-integral equation method), 128 radiative heat transfer, 299–300 Bilinear element, 97–98 and random walk, 258 Binary eutectic alloy: reflecting, 260 benchmark problem, 613–617 of the second kind, 56 diagram, 609 in sensitivity analysis, 452–457 Bioheat transfer, 851–887 of the third kind, 56 background for analysis of, 852–854 unsteady conduction, 75–79 blood vessel tissue-interactive numerical thermal Boundary-element method (BEM), 125–159, models, 864–866 924 burn injury modeling, 868–870 discretization of, 10 Chen and Holmes bioheat equation, 857–860 error estimation with, 158 continuum models of heat transfer, 861 for large-scale problems, 156–157 effective thermal conductivity, 855–856 major advantage of, 225 freezing of biological materials, 872–884 nomenclature related to, 158–159 bioheat equation for, 877–882 radiative heat transfer, 155–156 imaging-assisted numerical analysis, for steady heat conduction, 126–134 882–884 for steady heat conduction with generation, heating of living tissue, 868–872 134–139 hyperthermic treatment of cancer modeling, for transient conduction, 139–155 870–872 Boundary integral equation (BIE), 128 imaging-assisted numerical analysis, 882–884 Boundary-integral equation method (BIEM), 128 medical imaging interactive numerical analysis, Boundary problems (IHCP), 526 866–868 Boundary treatments: nomenclature related to, 885–887 control-volume-based finite-difference methods, Pennes equation, 856–857 212–215 finite-difference solution of, 863–864 control-volume-based finite-element methods, finite-element solution of, 861–863 215–217 Weinbaum-Jiji bioheat equation, 860–861 Boussinesq approximations, 735 948 INDEX Brick element, 110–112 adaptive mesh-refinement and mesh-coarsening, BTE, see Boltzmann transport equation 486, 488 Buoyancy effects: phase-change problems, 611–613 in continuous processing, 771 Coating process, optical fiber, 765, 767–768 data center airflow modeling, 826 Codes for numerical heat transfer, 936–941 in manufacturing processes modeling, commercial, 940–941 734–735 data exchange standards for, 938 under microgravity conditions, 775 data structures for, 936–937 Burn injury modeling, 868–870 programming languages and paradigms for, 937 public domain software resources for, 939 scripting language interface for, 938 C (programming language), 903 Verification of, 419–422, 438, 939–940 C++ (programming language), 903 Collaborative Adaptive Sensing of the Atmosphere CAD software, 474, 487 (CASA), 906–907 Calculations, Verification of, 419–422 Collocated equal-order CVFDMs/DVFEMs, 193 Cancer, hyperthermic treatment of, 870–872 Collocated interpolation schemes, 41–42 Capacitance matrix, 113 Collocated SIMPLE algorithm, 334–336 Carbon nanotubes, 681–689 Columnar solidification in static casting, 600–602, with fluids, 683–684 606 formation of, 681–682 Combustion systems, high-performance computing heat conduction of, 684–687 for, 900 thermal boundary resistance between surrounding Commercial codes, 940–941 materials and, 687–689 Complex-step method, 450–451 Carman-Kozeny relationship, 600, 603 Complex systems, Monte Carlo methods for, 274 Carravetta-Clementi (CC) potentials, 664–665 Composite materials: Carrier phase (two-phase flows), 699–700 polymer-matrix, 786–801 CASA, see Collaborative Adaptive Sensing of the thermoplastic-matrix, 792–801 Atmosphere consolidation stage, 792 Casting process, numerical modeling of, 767–770 fabrication of, 792–793 Cattaneo-Vernotte thermal wave model, 625–626, heat transfer, 793–797 634 prepregging stage, 792 CC potentials, see Carravetta-Clementi potentials spherulitic crystal microstructure evolution, Cell(mesh),7,9 797–801 Cell-based schemes, 9. See also Finite-volume thermosetting-matrix, 786–792 methods liquid composite molding, 767–789 Cell-centered FVMs, 192–193 pultrusion, 789–792 Cell centroid, 7 Compressible flow: Central limit theorem, 294 finite-difference methods, 85–88 Central moment, 294 multidomain spectral element method, 709–713 Certainty, level of, 422 pressure-based algorithms, 337–342 CFD, see Computational fluid dynamics at subsonic inlet, 345–347 CGM, see Conjugate gradient method at subsonic outlet, 347–348 CGSTAB, 38 Computational fluid dynamics (CFD), 4 Checkerboarding, 39, 41, 47 false diffusion in, 318 Chemically reactive flows, numerical modeling of, gradient-search techniques in, 37–38 736–738 iterative solution methods in, 31 Chemical vapor deposition (CVD), 732, 771–774 Computational grids, 907 Chen and Holmes (CH) bioheat equation, 857–860 Computational heat transfer (CHT), 4 Choice of solvers, 927 Computer room air conditioning (CRAC), 823, 825, CHT (computational heat transfer), 4 831 CIM, see Continuous interface method Computing: Circumcircle test, 476–477 grid, 899, 906–911 Clausius-Clapeyron relation, 702 improvement in, 896–897. See also Coarse-grid correction schemes, 69 High-performance computing Coarsening, 473 parallel, 896 adaptive grids, 486 Condensation coefficient, 674–675 INDEX 949 Conditional filtered diffusion, 173 Control-volume-based finite-difference methods Conduction: (CVFDMs): carbon nanotubes, 684–687 boundary treatments, 212–215 inverse problem for, 529–542 as cell-centered FVMs, 192 meshless methods for, 235–238 discretized equations: molecular dynamics method, 671–672 momentum, 208 Monte Carlo methods, 254 for pressure, 210 in solids, 672 for θ, 205–206 steady, 61–73 domain discretization, 194–196 boundary-element method, 126–139 features of, 192 discrete equations for, 458–460 formulations of, 192–193 finite-difference method, 61–73 governing differential equations, 193–194 finite-element method, 92–102 integral conservation equations, 197 Monte Carlo method, 263–265 interpolation functions, 198–201 unsteady, 73–79 mass-conserving velocity field equation, adiabatic boundary conditions, 78 209–210 convective boundary condition, 79 nomenclature related to, 220–222 Dirichlet boundary conditions, 77–78 sequential iterative variable adjustment implicit schemes, 77–79 procedure, 217–219 simple explicit scheme, 74–76 steady-state conduction, 62–64 specified boundary flux condition, 78–79 unsteady
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