Computational Fluid Dynamics: Principles and Applications

by Blazek

• ISBN13: 9780080430096
• ISBN10: 0080430090
• Edition: CD
• Format: Hardcover
• Copyright: 2001-05-11
• Publisher: Elsevier Science

Table of Contents

Acknowledgements	xi
List of Symbols	xiii
Abbreviations	xix
Introduction	1	(4)
Governing Equations	5	(24)
The Flow and its Mathematical Description	5	(3)
Conservation Laws	8	(5)
The Continuity Equation	8	(1)
The Momentum Equation	8	(2)
The Energy Equation	10	(3)
Viscous Stresses	13	(3)
Complete System of the Navier-Stokes Equations	16	(10)
Formulation for a Perfect Gas	18	(1)
Formulation for a Real Gas	19	(3)
Simplifications to the Navier-Stokes Equations	22	(4)
Bibliography	26	(3)
Principles of Solution of the Governing Equations	29	(46)
Spatial Discretisation	32	(13)
Finite Difference Method	36	(1)
Finite Volume Method	37	(2)
Finite Element Method	39	(1)
Other Discretisation Methods	40	(1)
Central versus Upwind Schemes	41	(4)
Temporal Discretisation	45	(8)
Explicit Schemes	46	(3)
Implicit Schemes	49	(4)
Turbulence Modelling	53	(3)
Initial and Boundary Conditions	56	(2)
Bibliography	58	(17)
Spatial Discretisation: Structured Finite Volume Schemes	75	(54)
Geometrical Quantities of a Control Volume	79	(4)
Two-Dimensional Case	79	(1)
Three-Dimensional Case	80	(3)
General Discretisation Methodologies	83	(10)
Cell-Centred Scheme	83	(2)
Cell-Vertex Scheme: Overlapping Control Volumes	85	(3)
Cell-Vertex Scheme: Dual Control Volumes	88	(3)
Cell-Centred versus Cell-Vertex Schemes	91	(2)
Discretisation of Convective Fluxes	93	(23)
Central Scheme with Artificial Dissipation	95	(3)
Flux-Vector Splitting Schemes	98	(7)
Flux-Difference Splitting Schemes	105	(3)
Total Variation Diminishing Schemes	108	(2)
Limiter Functions	110	(6)
Discretisation of Viscous Fluxes	116	(4)
Cell-Centred Scheme	118	(1)
Cell-Vertex Scheme	119	(1)
Bibliography	120	(9)
Spatial Discretisation: Unstructured Finite Volume Schemes	129	(52)
Geometrical Quantities of a Control Volume	134	(4)
Two-Dimensional Case	134	(1)
Three-Dimensional Case	135	(3)
General Discretisation Methodologies	138	(12)
Cell-Centred Scheme	139	(3)
Median-Dual Cell-Vertex Scheme	142	(4)
Cell-Centred versus Median-Dual Scheme	146	(4)
Discretisation of Convective Fluxes	150	(19)
Central Schemes with Artificial Dissipation	150	(4)
Upwind Schemes	154	(1)
Solution Reconstruction	154	(6)
Evaluation of Gradients	160	(5)
Limiter Functions	165	(4)
Discretisation of Viscous Fluxes	169	(5)
Element-Based Gradients	169	(2)
Average of Gradients	171	(3)
Bibliography	174	(7)
Temporal Discretisation	181	(44)
Explicit Time-Stepping Schemes	182	(8)
Multistage Schemes (Runge-Kutta)	182	(2)
Hybrid Multistage Schemes	184	(1)
Treatment of the Source Term	185	(1)
Determination of the Maximum Time Step	186	(4)
Implicit Time-Stepping Schemes	190	(22)
Matrix Form of Implicit Operator	191	(4)
Evaluation of the Flux Jacobian	195	(4)
ADI Scheme	199	(3)
LU-SGS Scheme	202	(6)
Newton-Krylov Method	208	(4)
Methodologies for Unsteady Flows	212	(4)
Dual Time-Stepping for Explicit Multistage Schemes	213	(2)
Dual Time-Stepping for Implicit Schemes	215	(1)
Bibliography	216	(9)
Turbulence Modelling	225	(42)
Basic Equations of Turbulence	228	(10)
Reynolds Averaging	229	(1)
Favre (Mass) Averaging	230	(1)
Reynolds-Averaged Navier-Stokes Equations	231	(1)
Favre-and Reynolds-Averaged Navier-Stokes Equations	232	(1)
Eddy-Viscosity Hypothesis	233	(2)
Non-Linear Eddy Viscosity	235	(1)
Reynolds-Stress Transport Equation	236	(2)
First-Order Closures	238	(10)
Spalart-Allmaras One-Equation Model	238	(3)
K-&epsis; Two-Equation Model	241	(4)
SST Two-Equation Model of Menter	245	(3)
Large-Eddy Simulation	248	(8)
Spatial Filtering	249	(1)
Filtered Governing Equations	250	(2)
Subgrid-Scale Modelling	252	(3)
Wall Models	255	(1)
Bibliography	256	(11)
Boundary Conditions	267	(32)
Concept of Dummy Cells	268	(2)
Solid Wall	270	(7)
Inviscid Flow	270	(5)
Viscous Flow	275	(2)
Farfield	277	(6)
Concept of Characteristic Variables	277	(2)
Modifications for Lifting Bodies	279	(4)
Inlet/Outlet Boundary	283	(2)
Symmetry Plane	285	(1)
Coordinate Cut	286	(1)
Periodic Boundaries	287	(3)
Interface Between Grid Blocks	290	(3)
Flow Gradients at Boundaries of Unstructured Grids	293	(1)
Bibliography	294	(5)
Acceleration Techniques	299	(32)
Local Time-Stepping	299	(1)
Enthalpy Damping	300	(1)
Residual Smoothing	301	(4)
Central IRS on Structured Grids	301	(2)
Central IRS on Unstructured Grids	303	(1)
Upwind IRS on Structured Grids	303	(2)
Multigrid	305	(15)
Basic Multigrid Cycle	306	(2)
Multigrid Strategies	308	(1)
Implementation on Structured Grids	309	(6)
Implementation on Unstructured Grids	315	(5)
Preconditioning for Low Mach Numbers	320	(4)
Bibliography	324	(7)
Consistency, Accuracy and Stability	331	(22)
Consistency Requirements	332	(1)
Accuracy of Discretisation	333	(1)
Von Neumann Stability Analysis	334	(16)
Fourier Symbol and Amplification Factor	334	(1)
Convection Model Equation	335	(1)
Convection-Diffusion Model Equation	336	(1)
Explicit Time-Stepping	337	(6)
Implicit Time-Stepping	343	(4)
Derivation of the CFL Condition	347	(3)
Bibliography	350	(3)
Principles of Grid Generation	353	(40)
Structured Grids	356	(11)
C-, H-, and O-Grid Topology	357	(2)
Algebraic Grid Generation	359	(4)
Elliptic Grid Generation	363	(2)
Hyperbolic Grid Generation	365	(2)
Unstructured Grids	367	(17)
Delaunay Triangulation	368	(5)
Advancing-Front Method	373	(1)
Generation of Anisotropic Grids	374	(5)
Mixed-Element/Hybrid Grids	379	(2)
Assessment and Improvement of Grid Quality	381	(3)
Bibliography	384	(9)
Description of the Source Codes	393	(8)
Programs for Stability Analysis	395	(1)
Structured 1-D Grid Generator	395	(1)
Structured 2-D Grid Generators	396	(1)
Structured to Unstructured Grid Converter	396	(1)
Quasi 1-D Euler Solver	396	(2)
Structured 2-D Euler Solver	398	(2)
Unstructured 2-D Euler Solver	400	(1)
Bibliography	400	(1)
A Appendix	401	(34)
A.1 Governing Equations in Differential Form	401	(6)
A.2 Mathematical Character of the Governing Equations	407	(4)
A.2.1 Hyperbolic Equations	407	(2)
A.2.1 Parabolic Equations	409	(1)
A.2.3 Elliptic Equations	409	(2)
A.3 Navier-Stokes Equations in Rotating Frame of Reference	411	(3)
A.4 Navier-Stokes Equations Formulated for Moving Grids	414	(2)
A.5 Thin Shear Layer Approximation	416	(2)
A.6 Parabolised Navier-Stokes Equations	418	(1)
A.7 Convective Flux Jacobian	419	(2)
A.8 Viscous Flux Jacobian	421	(3)
A.9 Transformation from Conservative to Characteristic Variables	424	(3)
A.10 GMRES Algorithm	427	(4)
A.11 Tensor Notation	431	(1)
Bibliography	432	(3)
Index	435