| Preface | p. xv |
| Numerical Techniques for Fluid Flows with Moving Boundaries | p. 1 |
| Introduction | p. 1 |
| Motivation | p. 1 |
| Overview of the Present Work | p. 3 |
| Numerical Methods Applied to General Moving Boundary Problems | p. 6 |
| Choice of Method-Lagrangian or Eulerian? | p. 8 |
| Review of Available Methods for Moving Boundary Problems | p. 8 |
| Transformation Methods with Body-Fitted Coordinates | p. 9 |
| Boundary Element Methods (BEM) | p. 9 |
| Volume Tracking Methods | p. 9 |
| The Level-Set Method | p. 10 |
| Moving Unstructured Boundary Conforming Grid Methods | p. 12 |
| Phase Field Models | p. 14 |
| Summary | p. 19 |
| Governing Equations and Solution Procedure | p. 21 |
| Formulation | p. 22 |
| Governing Equations | p. 22 |
| Governing Equations in a Body-Fitted Coordinate System | p. 23 |
| Discretization of the Conservation Laws | p. 24 |
| Pressure-Based Algorithm | p. 24 |
| Consistent Estimation of the Metric Terms | p. 32 |
| Illustrative Test Cases | p. 33 |
| Rotated Channel Flow | p. 33 |
| Uniform Flow Using a Moving Grid | p. 35 |
| Formulation and Solution of Flows with Free Surfaces | p. 36 |
| Introduction | p. 36 |
| Prediction of Meniscus Shapes | p. 39 |
| Methodology | p. 39 |
| Effect of Convection on Meniscus Shape | p. 42 |
| Sources of Convection | p. 43 |
| Natural Convection | p. 43 |
| Marangoni Convection | p. 43 |
| Nondimensionalization and Scaling Procedure | p. 44 |
| Heat Conduction Scales | p. 45 |
| Natural Convection Scales | p. 45 |
| The Marangoni Number | p. 45 |
| Formulation and Computational Algorithm for Transport Processes | p. 46 |
| Results and Discussion | p. 48 |
| Prediction of Meniscus Shapes | p. 48 |
| Heat Transfer Calculations | p. 51 |
| Numerical Procedure | p. 52 |
| Heat Conduction Only | p. 52 |
| Natural Convection | p. 53 |
| Interaction of Natural and Thermocapillary Convection | p. 54 |
| Effect of Convection on Meniscus Shape | p. 57 |
| Conclusions | p. 58 |
| Moving Grid Techniques: Fluid Membrane Interaction | p. 61 |
| Description of the Physical Problem | p. 61 |
| Potential Flow-Based Membrane Wing Models | p. 63 |
| Membrane Equilibrium | p. 65 |
| Nondimensionalization of the Governing Equations | p. 67 |
| The Moving Grid Computational Procedure | p. 70 |
| A Potential Flow Model for Thin Wings | p. 72 |
| Membrane Wings in Steady Flow | p. 74 |
| Effect of Outer Boundary Location | p. 74 |
| Classification of Flexible Membrane Wings | p. 76 |
| Elastic Membrane Case | p. 76 |
| Inextensible Membrane Case | p. 77 |
| Membrane Wings in Unsteady Flow | p. 80 |
| Constant Tension Membrane Case | p. 82 |
| Elastic Membrane Case | p. 82 |
| Inextensible Membrane Case | p. 86 |
| Summary and Conclusion | p. 93 |
| Moving Grid Techniques: Modeling Solidification Processes | p. 95 |
| Introduction | p. 95 |
| Morphological Instabilities During Solidification | p. 95 |
| Physics of Morphological Instabilities in Solidification | p. 98 |
| Implications of Morphological Instabilities | p. 103 |
| Need for Numerical Techniques | p. 105 |
| Requirements of the Numerical Method | p. 107 |
| Application of the Boundary-Fitted Approach | p. 108 |
| Formulation | p. 109 |
| Assessment of the Quasi-stationary Approximation | p. 112 |
| A General Procedure for Interface Tracking | p. 113 |
| Results and Discussion | p. 115 |
| Case 1. Calculations with Temperature Field Active in One Phase Only | p. 115 |
| Case 2. Calculations with Temperature Field Active in Both Phases | p. 116 |
| Motion of Curved Fronts | p. 117 |
| Interfacial Conditions | p. 117 |
| Scales for the Morphological Instability Simulations | p. 120 |
| Features of the Computational Method | p. 122 |
| Results and Discussion | p. 123 |
| Issues of Scaling and Computational Efficiency | p. 128 |
| Choice of Reference Scales and Resulting Equations | p. 129 |
| Conclusions | p. 130 |
| Fixed Grid Techniques: Enthalpy Formulation | p. 135 |
| Governing Equations | p. 135 |
| Scaling Issues | p. 136 |
| The Macroscopic Scales | p. 139 |
| Velocity Scales | p. 141 |
| Thermal Scales | p. 143 |
| Low Prandtl Number (Metallic Melts) | p. 143 |
| High Prandtl Number (Organic Melts) | p. 144 |
| The Morphological Scales | p. 146 |
| Pure Conduction | p. 147 |
| Morphological Scales in the Presence of Convection | p. 149 |
| Low Prandtl Number Melts | p. 149 |
| High Prandtl Number Melts | p. 150 |
| Enthalpy Formulation | p. 151 |
| Heat Conduction | p. 152 |
| Implementation | p. 155 |
| Implementation of the T-Based Method | p. 155 |
| Implementation of the H-Based Method | p. 156 |
| Results and Discussion | p. 156 |
| Accuracy Assessment | p. 156 |
| Performance Assessment | p. 158 |
| Summary | p. 163 |
| Convective Effects | p. 163 |
| Governing Equations | p. 163 |
| Source Terms in the Momentum Equations | p. 164 |
| Sources of Convection | p. 165 |
| Computational Procedure | p. 166 |
| Bridgman Growth of CdTe | p. 166 |
| Multi-Zone Simulation of Bridgman Growth Process | p. 171 |
| Governing Equations | p. 173 |
| Two-Level Modeling Strategy | p. 177 |
| The Global Furnace Simulation | p. 177 |
| The Refined Ampoule Simulation | p. 178 |
| Float Zone Growth of NiAl | p. 184 |
| Calculation Procedure | p. 185 |
| Results and Discussion | p. 187 |
| Heat Conduction | p. 187 |
| Thermocapillary Convection | p. 188 |
| Summary | p. 192 |
| Fixed Grid Techniques: ELAFINT-Eulerian-Lagrangian Algorithm For INterface Tracking | p. 195 |
| Introduction | p. 195 |
| Interface Tracking Procedure | p. 197 |
| Basic Methodology | p. 198 |
| Procedures for Mergers/Breakups | p. 202 |
| Solution of the Field Equations | p. 211 |
| Control Volume Formulation with Moving Interface with Moving Interface | p. 211 |
| The Control Volume Formulation for a Transport Variable | p. 213 |
| Discretization | p. 213 |
| Treatment of Variables on the Staggered Grid | p. 216 |
| Computation of Convective Fluxes | p. 216 |
| Evaluation of the Diffusion and the Full Discretized Form | p. 217 |
| Evaluation of the Source Term | p. 220 |
| Computation of Interfacial Fluxes | p. 221 |
| Computation of the Pressure Field | p. 227 |
| Computing the Velocities of the Interfacial Markers | p. 228 |
| Dealing with Cut Cells | p. 228 |
| Conservation and Consistency at Cell Faces | p. 229 |
| Anomalous Cases | p. 229 |
| Distinction Between Liquid and Solid Cells | p. 231 |
| Moving Boundary Problems-Treatment of Cells That Change Phase | p. 232 |
| Results for Pure Conduction | p. 232 |
| Grid Addition/Deletion | p. 233 |
| Planar Interface Propagation | p. 234 |
| Non-planar Interfaces | p. 235 |
| Zero Surface Tension | p. 236 |
| Low Surface Tension | p. 238 |
| Stable Fingers for Significant Surface Tension | p. 241 |
| Summary | p. 244 |
| Assessment of Fixed Grid Techniques | p. 249 |
| Introduction | p. 249 |
| Results for Stationary Boundaries | p. 249 |
| Melting from a Vertical Wall | p. 250 |
| Summary | p. 259 |
| Concluding Remarks | p. 260 |
| References | p. 261 |
| Index | p. 281 |
| Table of Contents provided by Ingram. All Rights Reserved. |
