Essentials of Computational Fluid Dynamics

Foreword -- 1 Introduction -- 1.1 CFD, the virtual wind tunnel -- 1.2 Examples of CFD applications -- 1.3 Prerequisites -- 1.4 Literature -- 1.5 Ingredients -- 1.6 Organisation of the chapters -- 1.7 Exercises -- 2 Physical and mathematical principles of modern CFD -- 2.1 The physical model -- 2.1.1 Continuum assumption -- 2.1.2 Lagrangian vs. Eulerian description -- 2.1.3 Conservation principles -- 2.2 The mathematical model: the equations of fluid flow -- 2.2.1 Mass conservation in 1-D -- 2.2.2 Mass conservation in 3-D -- 2.2.3 Divergence and gradient operators, total derivative -- 2.2.4 The total or material derivative -- 2.2.5 The divergence form of the total derivative -- 2.2.6 Reynolds' transport theorem -- 2.2.7 Transport of a passive scalar -- 2.3 The momentum equations -- 2.3.1 Examples of momentum balance -- 2.3.2 The inviscid momentum equation - the Euler equation -- 2.3.3 The viscous momentum equations - Navier-Stokes -- 2.3.4 The incompressible Navier-Stokes equations -- 2.3.5 Energy balance -- 2.3.6 Summary of properties for the Navier-Stokes equations -- 2.4 Simplified model equations -- 2.4.1 Linear advection equation -- 2.4.2 Inviscid Burgers' equation -- 2.4.3 Heat equation -- 2.5 Excercises -- 3 Discretisation of the equations -- 3.1 Discretisation of the linear advection equation -- 3.1.1 Finite difference discretisation of linear advection . -- 3.1.2 Solving the finite difference approximation -- 3.1.3 Mesh refinement -- 3.1.4 Finite volume discretisation of the 1-D advection . -- 3.1.5 Solving the finite volume approximation -- 3.1.6 Finite difference vs. finite volume formulations . . -- 3.2 Burgers' equation: non-linear advection and conservation -- 3.3 Heat equation in 1-D -- 3.3.1 Discretising second derivatives -- 3.3.2 1-D Heat equation, differential form -- 3.3.3 Solving the 1-D heat equation -- 3.4 Advection equation in 2-D -- 3.4.1 Discretisation on a structured grid -- 3.5 Solving the Navier-Stokes equations -- 3.6 The main steps in the finite volume method -- 3.6.1 Discretisation on arbitrary grids -- 3.6.2 Transport through an arbitrary face -- 3.6.3 The concept of pseudotime-stepping -- 3.6.4 Time-stepping for compressible flows -- 3.6.5 Iterative methods for incompressible flows -- 3.6.6 The SIMPLE scheme -- 3.7 Exercises -- 4 Analysis of discretisations -- 4.1 Forward, backward and central differences -- 4.2 Taylor analysis: consistency, first- and second-order accuracy -- 4.2.1 Round-off errors -- 4.2.2 Order of accuracy and mesh refinement -- 4.3 Stability, artificial viscosity and second-order accuracy . . -- 4.3.1 Artificial viscosity -- 4.3.2 Artificial viscosity and finite volume methods -- 4.3.3 Stable second-order accurate discretisations for CFD -- 4.3.4 Monotonicity and second-order accuracy: limiters . -- 4.4 Summary of spatial discretisation approaches -- 4.5 Convergence of the time-stepping iterations -- 4.5.1 Explicit methods -- 4.5.2 Implicit methods -- 4.5.3 Increasing mesh resolution -- 4.5.4 Multigrid -- 4.6 Excercises -- 5 Boundary conditions and flow physics -- 5.1 Selection of boundary conditions -- 5.1.1 Some simple examples -- 5.1.2 Selecting boundary conditions to satisfy the equations -- 5.2 Characterisation of partial differential equations -- 5.2.1 Wave-like solutions: hyperbolic equations -- 5.2.2 Smoothing-type solutions: elliptic equations -- 5.2.3 The borderline case - parabolic equations -- 5.2.4 The domain of dependence, the domain of influence -- 5.2.5 Example of characterisation: surface waves -- 5.2.6 Compressible and incompressible flows -- 5.2.7 Characterisation of the Navier-Stokes equations . . -- 5.3 Choice of boundary conditions -- 5.3.1 Boundary conditions for incompressible flow -- 5.3.2 Boundary conditions for hyperbolic equations -- 5.4 Exercises -- 6 Turbulence modelling -- 6.1 The challenges of turbulent flow for CFD -- 6.2 Description of turbulent flow -- 6.3 Self-similar profiles through scaling -- 6.3.1 Laminar velocity profiles -- 6.3.2 Turbulent velocity profile -- 6.4 Velocity profiles of turbulent boundary layers -- 6.4.1 Outer scaling: friction velocity -- 6.4.2 Inner scaling: non-dimensional wall distance y+ -- 6.5 Levels of turbulence modelling -- 6.5.1 Direct Numerical Simulation (DNS) -- 6.5.2 Reynolds-Averaged Navier-Stokes (RANS) -- 6.5.3 Large Eddy (LES) & Detached Eddy Simulation (DES) -- 6.5.4 Summary of approaches to turbulence modelling . -- 6.6 Eddy viscosity models -- 6.6.1 Mixing length model -- 6.6.2 The Spalart-Allmaras model -- 6.6.3 The k-e model -- 6.7 Near-wall mesh requirements -- 6.7.1 Estimating the wall distance of the first point -- 6.8 Exercises -- 7 Mesh quality and grid generation -- 7.1 Influence of mesh quality on the accuracy -- 7.1.1 Maximum angle condition -- 7.1.2 Regularity -- 7.1.3 Size variation -- 7.2 Requirements for the ideal mesh generator -- 7.3 Structured grids -- 7.3.1 Algebraic grids using transfinite interpolation -- 7.4 Unstructured grids -- 7.4.1 The Advancing Front Method -- 7.4.2 Delaunay triangulation -- 7.4.3 Hierarchical grid Methods -- 7.4.4 Hexahedral unstructured mesh generation -- 7.4.5 Hybrid mesh generation for viscous flow -- 7.5 Mesh adaptation -- 7.5.1 Mesh movement: r-refinement -- 7.5.2 Mesh refinement: h-refinement -- 7.6 Exercises -- 8 Analysis of the results -- 8.1 Types of errors -- 8.1.1 Incorrect choice of boundary conditions -- 8.1.2 Insufficient convergence -- 8.1.3 Artificial viscosity -- 8.1.4 Modelling errors -- 8.2 Mesh convergence -- 8.2.1 Cost of error reduction -- 8.3 Validation -- 8.4 Summary -- 8.5 Exercises -- 9 Case studies -- 9.1 Aerofoil in 2-D, inviscid flow -- 9.1.1 Case description -- 9.1.2 Flow physics -- 9.1.3 Meshes -- 9.1.4 Simulation results for the C-mesh -- 9.1.5 Comparison of C- vs O-mesh -- 9.1.6 Analysis of lift and drag values -- 9.2 Blood vessel bifurcation in 2-D -- 9.2.1 Geometry and flow parameters -- 9.2.2 Flow physics and boundary conditions -- 9.2.3 Velocity and pressure fields -- 9.2.4 Velocity profile in the neck -- 9.2.5 Effect of outlet boundary condition -- 9.3 Aerofoil in 2-D, viscous flow -- 9.3.1 Flow physics -- 9.3.2 Turbulence modelling -- 9.3.3 Flow results -- 9.3.4 Lift and drag -- 10 Appendix -- 10.1 Finite-volume implementation of 2-D advection -- Bibliography -- Index.

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• Mecânica dos fluidos
• Dinâmica e estática

Finite Difference Method;CFL Condition;CFD;CFL Number;Virtual Windtunnel;Compressible Flow Equations;Simplified Model Equations;Linear Advection Equation;Discretisation of the linear advection equation;Artificial Viscosity;Discretization;Velocity Magnitude Contours;Burgers' Equation;2nd C256;Heat equation in 1D;Multi-block Mesh;Advection Equation in 2D;RANS Model;Navier-Stokes Equations;Cfd Solution;The Finite Volume Method;Finite Volume Method;Forward, Backward and Central Differences;Error Modes;Taylor Analysis;Pressure Correction Equation;First- and Second-Order Accuracy;Spalart Allmaras Model;Stability and Artificial Viscosity;Upwind Scheme;Second-Order Accuracy;Advection Speed;Spatial Discretisation Approaches;Advection Equation;Convergence of the Time-Stepping Iterations;Truncation Error;Boundary Conditions;Block Profile;Flow Physics;Wall Shear Stress;PDEs;Slip Wall Condition;Turbulence Modelling;Unsteady Turbulence;Turbulence Modeling;Tetrahedral Mesh;Turbulent Flow;Boundary Condition Setup;Turbulent Boundary Layers;Eddy Viscosity Models;Near-Wall Mesh Requirements;Mesh Quality;Grid Generation;Mesh Generator;Structured Grids;Unstructured Grids;Mesh Adaptation;Mesh Convergence;Validation;Aerofoil in 2-D, Inviscid Flow;Blood Vessel Bifurcation in 2-D;Aerofoil in 2-D, Viscous Flow;Finite-Volume Implementation of 2-D Advection