Computational Thermo-Fluid Dynamics -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 Heat and Fluid Flows in Materials Science and Engineering -- 1.2 Overview of the Present Work -- 2 Mathematical Description of Physical Phenomena in Thermofluid Dynamics -- 2.1 Conservation Equations for Continuum Media -- 2.1.1 Conservation of Mass -- 2.1.2 Conservation of Momentum -- 2.1.3 Energy Conservation Equation -- 2.1.4 Conservation of Chemical Species -- 2.1.5 Boussinesq Approximation -- 2.1.6 Unified Form of Conservation Equations -- 2.1.7 Nondimensional Form of Conservation Equations -- 2.1.8 Short Summary -- 2.2 Boundary and Initial Conditions -- 2.2.1 Heat Transfer -- 2.2.2 Solutal Transfer -- 2.2.3 Fluid Dynamics -- 2.3 Conservation Equations in Electromagnetics -- 2.3.1 Maxwell Equations -- 2.3.2 Induction and Poisson Equations -- 2.3.3 An Example of a Low Magnetic Reynolds Number Approximation: Rotating Magnetic Field -- 3 Discretization Approaches and Numerical Methods -- 3.1 The Finite Difference Method -- 3.1.1 Introduction -- 3.1.2 Approximation Schemes -- 3.1.3 Example of Conservative Property of FDM -- 3.1.4 Discretization Schemes of Unsteady Equations -- 3.1.5 Example of Unsteady Diffusion Equation -- 3.2 The Finite Volume Method -- 3.2.1 Basic Concept -- 3.2.2 Interpolation Schemes -- 3.2.3 Linearized Form of Discretized Conservation Equation -- 3.2.4 Treatment of Source Terms -- 3.2.5 Boundary Conditions -- 3.2.6 Comparative Study of Schemes for One-Dimensional Convection/Diffusion Problem -- 3.3 Solution of Linear Equation Systems -- 3.3.1 Direct Methods -- 3.3.2 Iterative Methods -- 3.3.3 Residuals and Convergence -- 3.3.4 Multigrid Method -- 3.3.5 Illustration of Iterative Methods -- 4 Calculations of Flows with Heat and Mass Transfer -- 4.1 Solution of Incompressible Navier-Stokes Equations.

4.2 Pressure and Velocity Coupling: SIMPLE Family -- 4.2.1 SIMPLE -- 4.2.2 SIMPLER -- 4.2.3 SIMPLE with Collocated Variables Arrangement -- 4.3 Illustrations of Schemes for Flow with Heat Transfer -- 4.4 Complex Geometry Problems on Fixed Cartesian Grids -- 4.4.1 Immersed Boundary Methods -- 4.4.2 Cartesian Grid Methods -- 4.4.3 Immersed Surface Reconstruction -- 4.4.4 Illustration of Continuous-Forcing IBM -- 5 Convection-Diffusion Phase-Change Problems -- 5.1 Some Aspects of Solidification Thermodynamics -- 5.1.1 One-Component Melts -- 5.1.2 Binary Alloys -- 5.1.3 Interface and Equilibrium -- 5.2 Modeling of Macroscale Phase-Change Phenomena -- 5.2.1 Heat Transfer in Phase-Change Systems: Fixed and Moving Grids -- 5.2.2 Mathematical Models of a Binary Alloy Solidification -- 5.2.3 Closure Relations for the Volume Fraction of Liquid -- 5.3 Turbulent Solidification -- 5.3.1 Review of Unsteady RANS Modeling of a Solidification -- 5.3.2 Conditions for the DNS of Convection-Driven Solidification -- 5.4 Microscale Phase-Change Phenomena -- 5.4.1 Basic Modeling Concepts -- 5.4.2 Modified Cellular Automaton Model -- 5.4.3 Virtual Interface Tracking Model -- 5.5 Modeling of Crystal Growth -- 5.5.1 Modeling Approaches -- 5.5.2 RMF Control of Crystal Growth -- 5.5.3 Model Formulation and Validation Case -- 5.5.4 VGF-RMF Crystal Growth -- 5.6 Melting of Pure Calium under the Influence of Natural Convection -- 5.6.1 State of Modeling -- 5.6.2 Model and Numerical Description -- 5.6.3 Results and Discussions -- 6 Application I: Spin-Up of a Liquid Metal in Cylindrical Cavities -- 6.1 Spin-Up of Isothermal Flow Driven by a Rotating Magnetic Field -- 6.1.1 Model Formulation -- 6.1.2 Governing Equations and Characteristic Scales -- 6.1.3 Numerical Techniques and Code Validation -- 6.1.4 The Physical Nature of Axisymmetric Instability -- 6.1.5 Numerical Results.

6.1.6 Discussions -- 6.1.7 Short Summary -- 6.2 Impact of Buoyancy Force on Spin-Up Dynamics -- 7 Application II: Laminar and Turbulent Flows Driven by an RMF -- 7.1 Laminar Flows: State of the Art -- 7.1.1 Problem Formulation -- 7.1.2 Numerical Method -- 7.1.3 Numerical Results -- 7.1.4 Discussion -- 7.1.5 Short Summary -- 7.1.6 Estimation of Critical Taylor Number -- 7.2 Turbulent Flows -- 7.2.1 Axisymmetric Numerical Simulations -- 7.2.2 RANS: k- Turbulence Model -- 8 Application III: Contactless Mixing of Liquid Metals -- 8.1 Mixing under Zero-Gravity Conditions -- 8.1.1 Problem Formulation and Main Simplifications -- 8.1.2 Numerical Scheme and Validation Tests -- 8.1.3 Numerical Results -- 8.1.4 Discussion of Different Mixing Scenarios -- 8.1.5 Short Summary -- 8.2 The Impact of Gravity on Mixing -- 9 Application IV: Electromagnetic Control of Binary Metal Alloys Solidification -- 9.1 Control of a Binary Metal Alloy Solidification by Use of Alternating Current Fields -- 9.1.1 Control of Unidirectional Solidification of Al-Si Alloy by Use of RMF -- 9.1.2 Control of Side Cooled Systems by Use of RMF and TMF -- 9.2 Control of Solidification by Use of Steady Electromagnetic Fields -- 9.2.1 Problem and Model Formulation -- 9.2.2 Validation Test Cases -- 9.2.3 Numerical Results -- 9.3 The Impact of a Steady Electrical Current on Unidirectional Solidification -- 9.3.1 Problem and Model Formulation -- 9.3.2 Numerical Results and Discussions -- 9.4 The Impact of an Electric Field on the Shape of a Dendrite -- 9.4.1 Problem and Model Formulation -- 9.4.2 Scaling for Electrovortex Flows -- 9.4.3 Numerical Method and Code Validation -- 9.4.4 Numerical Results -- 9.5 The Impact of Parallel Applied Electric and Magnetic Fields on Dendritic Growth -- 9.5.1 Problem and Model Formulation -- 9.5.2 Numerical Results -- References -- Index.