Kooperativer Bibliotheksverbund

UID:

Format: 1 online resource (466 pages) : , illustrations

Edition: Third edition.

ISBN: 0-08-099995-6 , 0-12-801172-6

Content: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques.

Note: Front Cover -- Computational Fluid Dynamics: Principles and Applications -- Copyright -- Contents -- Acknowledgments -- List of Symbols -- Abbreviations -- Chapter 1: Introduction -- Chapter 2: Governing Equations -- 2.1 The Flow and Its Mathematical Description -- 2.1.1 Finite control volume -- 2.2 Conservation Laws -- 2.2.1 The continuity equation -- 2.2.2 The momentum equation -- 2.2.3 The energy equation -- 2.3 Viscous Stresses -- 2.4 Complete System of the Navier-Stokes Equations -- 2.4.1 Formulation for a perfect gas -- 2.4.2 Formulation for a real gas -- 2.4.3 Simplifications to the Navier-Stokes equations -- Thin shear layer approximation -- Parabolized Navier-Stokes equations -- Euler equations -- References -- Chapter 3: Principles of Solution of the Governing Equations -- 3.1 Spatial Discretization -- 3.1.1 Finite-difference method -- 3.1.2 Finite-volume method -- 3.1.3 Finite-element method -- 3.1.4 Other discretization methods -- Spectral-element method -- Lattice Boltzmann method -- Gridless method -- 3.1.5 Central and upwind schemes -- Central schemes -- Upwind schemes -- Flux-vector splitting schemes -- Flux-difference splitting schemes -- TVD Schemes -- Fluctuation-splitting schemes -- Solution reconstruction -- First- and second-order schemes -- ENO/WENO Schemes -- Central versus upwind schemes -- Upwind schemes for real gas flows -- 3.2 Temporal Discretization -- 3.2.1 Explicit schemes -- 3.2.2 Implicit schemes -- 3.3 Turbulence Modeling -- 3.4 Initial and Boundary Conditions -- References -- Chapter 4: Structured Finite-Volume Schemes -- 4.1 Geometrical Quantities of a Control Volume -- 4.1.1 Two-dimensional case -- 4.1.2 Three-dimensional case -- 4.2 General Discretization Methodologies -- 4.2.1 Cell-centered scheme -- 4.2.2 Cell-vertex scheme: overlapping control volumes -- 4.2.3 Cell-vertex scheme: dual control volumes. , 4.2.4 Cell-centered versus cell-vertex schemes -- 4.3 Discretization of the Convective Fluxes -- 4.3.1 Central scheme with artificial dissipation -- Scalar dissipation scheme -- Matrix dissipation scheme -- 4.3.2 Flux-vector splitting schemes -- Van Leer's scheme -- AUSM -- CUSP scheme -- 4.3.3 Flux-difference splitting schemes -- Roe upwind scheme -- 4.3.4 Total variation diminishing schemes -- Upwind TVD scheme -- 4.3.5 Limiter functions -- Limiter functions for MUSCL interpolation -- MUSCL scheme with =0 -- MUSCL scheme with =1/3 -- Limiter for CUSP scheme -- Limiter for TVD scheme -- 4.4 Discretization of the Viscous Fluxes -- 4.4.1 Cell-centered scheme -- 4.4.2 Cell-vertex scheme -- References -- Chapter 5: Unstructured Finite-Volume Schemes -- 5.1 Geometrical Quantities of a Control Volume -- 5.1.1 Two-dimensional case -- Triangular element -- Quadrilateral element -- Element center -- 5.1.2 Three-dimensional case -- Triangular face -- Quadrilateral face -- Volume -- Cell centroid -- 5.2 General Discretization Methodologies -- 5.2.1 Cell-centered scheme -- 5.2.2 Median-dual cell-vertex scheme -- 5.2.3 Cell-centered versus median-dual scheme -- Accuracy -- Computational work -- Memory requirements -- Grid generation/adaptation -- 5.3 Discretization of the Convective Fluxes -- 5.3.1 Central scheme with artificial dissipation -- 5.3.2 Upwind schemes -- 5.3.3 Solution reconstruction -- Reconstruction based on MUSCL approach -- Piecewise linear reconstruction -- Linear reconstruction based on nodal weighting procedure -- Piecewise quadratic reconstruction -- 5.3.4 Evaluation of the gradients -- Green-Gauss approach -- Median-dual scheme -- Cell-centered scheme -- Mixed grids -- Least-squares approach -- 5.3.5 Limiter functions -- Limiter of Barth and Jespersen -- Venkatakrishnan's limiter -- 5.4 Discretization of the Viscous Fluxes. , 5.4.1 Element-based gradients -- Face-centered control volume -- Approximate Galerkin finite-element approach -- Average of nodal values -- 5.4.2 Average of gradients -- References -- Chapter 6: Temporal Discretization -- 6.1 Explicit Time-Stepping Schemes -- 6.1.1 Multistage schemes (Runge-Kutta) -- 6.1.2 Hybrid multistage schemes -- 6.1.3 Treatment of the source term -- 6.1.4 Determination of the maximum time step -- Time step on structured grids -- Euler equations -- Navier-Stokes equations -- Time step on unstructured grids -- Method 1 -- Method 2 -- 6.2 Implicit Time-Stepping Schemes -- 6.2.1 Matrix form of the implicit operator -- Implicit operator on structured grids -- Implicit operator on unstructured grids -- 6.2.2 Evaluation of the flux Jacobian -- Central scheme -- Flux-vector splitting scheme -- Flux-difference splitting scheme -- Viscous flows -- 6.2.3 Alternating direction implicit scheme -- 6.2.4 Lower-upper symmetric Gauss-Seidel scheme -- LU-SGS on structured grids -- LU-SGS on unstructured grids -- 6.2.5 Newton-Krylov method -- GMRES method -- Computation of the flux Jacobian -- Preconditioning -- Start-up problem -- 6.2.6 Implicit Runge-Kutta schemes -- 6.3 Methodologies for Unsteady Flows -- 6.3.1 Dual time-stepping for explicit multistage schemes -- 6.3.2 Dual time-stepping for implicit schemes -- References -- Chapter 7: Turbulence Modeling -- 7.1 Basic Equations of Turbulence -- 7.1.1 Reynolds averaging -- 7.1.2 Favre (mass) averaging -- 7.1.3 Reynolds-averaged Navier-Stokes equations -- 7.1.4 Favre- and Reynolds-averaged Navier-Stokes equations -- 7.1.5 Eddy-viscosity hypothesis -- 7.1.6 Non-linear eddy viscosity -- 7.1.7 Reynolds-stress transport equation -- 7.2 First-Order Closures -- 7.2.1 Spalart-Allmaras one-equation model -- Differential form -- Integral form -- Initial and boundary conditions. , 7.2.2 K - two-equation model -- Differential form -- Integral form -- Initial and boundary conditions -- Wall functions -- 7.2.3 SST two-equation model of Menter -- Differential form -- Boundary conditions -- 7.3 Large-Eddy Simulation -- 7.3.1 Spatial filtering -- 7.3.2 Filtered governing equations -- Incompressible Navier-Stokes equations -- Compressible Navier-Stokes equations -- 7.3.3 Subgrid-scale modeling -- Eddy-viscosity models -- Smagorinsky SGS model -- Dynamic SGS models -- 7.3.4 Wall models -- 7.3.5 Detached eddy simulation -- References -- Chapter 8: Boundary Conditions -- 8.1 Concept of Dummy Cells -- 8.2 Solid Wall -- 8.2.1 Inviscid flow -- Structured cell-centered scheme -- Structured cell-vertex scheme -- Unstructured cell-centered scheme -- Unstructured median-dual scheme -- 8.2.2 Viscous flow -- Cell-centered scheme -- Cell-vertex scheme -- 8.3 Far-Field -- 8.3.1 Concept of characteristic variables -- Supersonic inflow -- Supersonic outflow -- Subsonic inflow -- Subsonic outflow -- 8.3.2 Modifications for lifting bodies -- Vortex correction in 2D -- Vortex correction in 3D -- 8.4 Inlet/Outlet Boundary -- Subsonic inlet -- Subsonic outlet -- Supersonic inlet and outlet -- 8.5 Injection Boundary -- 8.6 Symmetry Plane -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- 8.7 Coordinate Cut -- 8.8 Periodic Boundaries -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- Rotational periodicity -- 8.9 Interface Between Grid Blocks -- 8.10 Flow Gradients at Boundaries of Unstructured Grids -- References -- Chapter 9: Acceleration Techniques -- 9.1 Local Time-Stepping -- 9.2 Enthalpy Damping -- 9.3 Residual Smoothing -- 9.3.1 Central IRS on structured grids -- 9.3.2 Central IRS on unstructured grids -- 9.3.3 Upwind IRS on structured grids -- 9.4 Multigrid -- 9.4.1 Basic multigrid cycle. , Transfer of the solution and residuals to the coarser grid -- Computation of a new solution on the coarse grid -- Solution interpolation from the coarse to the fine grid -- 9.4.2 Multigrid strategies -- Number of time steps -- Starting grid -- Accuracy of transfer operators -- 9.4.3 Implementation on structured grids -- Transfer operators for the cell-centered scheme -- Transfer operators for the cell-vertex scheme -- Upwind prolongation (cell-vertex scheme) -- 9.4.4 Implementation on unstructured grids -- Nonnested grids -- Topological methods -- Agglomeration multigrid method -- Generation of coarse grids by volume agglomeration -- Problems of agglomeration multigrid -- 9.5 Preconditioning for Low Mach Numbers -- 9.5.1 Derivation of preconditioned equations -- 9.5.2 Implementation -- 9.5.3 Form of the matrices -- Transformation matrices -- Preconditioning matrices -- Weiss and Smith preconditioner -- Eigenvalues of the preconditioned system -- Eigenvectors of the preconditioned system -- 9.6 Parallelization -- 9.6.1 MPI -- 9.6.2 OpenMP -- 9.6.3 CUDA -- 9.6.4 OpenCL -- References -- Chapter 10: Consistency, Accuracy, and Stability -- 10.1 Consistency Requirements -- 10.2 Accuracy of Discretization Scheme -- 10.3 Von Neumann Stability Analysis -- 10.3.1 Fourier symbol and amplification factor -- 10.3.2 Convection model equation -- Central scheme with artificial dissipation -- Upwind scheme -- 10.3.3 Convection-diffusion model equation -- 10.3.4 Explicit time-stepping -- Examples of Fourier symbols and amplification factors -- 10.3.5 Implicit time-stepping -- Examples of amplification factors -- 10.3.6 Derivation of the CFL condition -- CFL condition by von Neumann analysis -- References -- Chapter 11: Principles of Grid Generation -- 11.1 Structured Grids -- 11.1.1 C-, H-, and O-grid topology -- C-grid topology -- H-grid topology -- O-grid topology. , 11.1.2 Algebraic grid generation.

Language: English

Keywords: Electronic books.

URL: Click to View

UID:

Format: 1 online resource (XVIII, 447 Seiten) , Diagramme

Edition: Third edition

ISBN: 9780128011720 , 0128011726 , 9780080999951

Note: Includes bibliographical references and index , Front Cover; Computational Fluid Dynamics: Principles and Applications; Copyright; Contents; Acknowledgments; List of Symbols; Abbreviations; Chapter 1: Introduction; Chapter 2: Governing Equations; 2.1 The Flow and Its Mathematical Description; 2.1.1 Finite control volume; 2.2 Conservation Laws; 2.2.1 The continuity equation; 2.2.2 The momentum equation; 2.2.3 The energy equation; 2.3 Viscous Stresses; 2.4 Complete System of the Navier-Stokes Equations; 2.4.1 Formulation for a perfect gas; 2.4.2 Formulation for a real gas; 2.4.3 Simplifications to the Navier-Stokes equations , Thin shear layer approximationParabolized Navier-Stokes equations; Euler equations; References; Chapter 3: Principles of Solution of the Governing Equations; 3.1 Spatial Discretization; 3.1.1 Finite-difference method; 3.1.2 Finite-volume method; 3.1.3 Finite-element method; 3.1.4 Other discretization methods; Spectral-element method; Lattice Boltzmann method; Gridless method; 3.1.5 Central and upwind schemes; Central schemes; Upwind schemes; Flux-vector splitting schemes; Flux-difference splitting schemes; TVD Schemes; Fluctuation-splitting schemes; Solution reconstruction , First- and second-order schemesENO/WENO Schemes; Central versus upwind schemes; Upwind schemes for real gas flows; 3.2 Temporal Discretization; 3.2.1 Explicit schemes; 3.2.2 Implicit schemes; 3.3 Turbulence Modeling; 3.4 Initial and Boundary Conditions; References; Chapter 4: Structured Finite-Volume Schemes; 4.1 Geometrical Quantities of a Control Volume; 4.1.1 Two-dimensional case; 4.1.2 Three-dimensional case; 4.2 General Discretization Methodologies; 4.2.1 Cell-centered scheme; 4.2.2 Cell-vertex scheme: overlapping control volumes; 4.2.3 Cell-vertex scheme: dual control volumes , 4.2.4 Cell-centered versus cell-vertex schemes4.3 Discretization of the Convective Fluxes; 4.3.1 Central scheme with artificial dissipation; Scalar dissipation scheme; Matrix dissipation scheme; 4.3.2 Flux-vector splitting schemes; Van Leer's scheme; AUSM; CUSP scheme; 4.3.3 Flux-difference splitting schemes; Roe upwind scheme; 4.3.4 Total variation diminishing schemes; Upwind TVD scheme; 4.3.5 Limiter functions; Limiter functions for MUSCL interpolation; MUSCL scheme with =0; MUSCL scheme with =1/3; Limiter for CUSP scheme; Limiter for TVD scheme; 4.4 Discretization of the Viscous Fluxes , 4.4.1 Cell-centered scheme4.4.2 Cell-vertex scheme; References; Chapter 5: Unstructured Finite-Volume Schemes; 5.1 Geometrical Quantities of a Control Volume; 5.1.1 Two-dimensional case; Triangular element; Quadrilateral element; Element center; 5.1.2 Three-dimensional case; Triangular face; Quadrilateral face; Volume; Cell centroid; 5.2 General Discretization Methodologies; 5.2.1 Cell-centered scheme; 5.2.2 Median-dual cell-vertex scheme; 5.2.3 Cell-centered versus median-dual scheme; Accuracy; Computational work; Memory requirements; Grid generation/adaptation

Language: English

Subjects: Physics , Mathematics

Keywords: Numerische Strömungssimulation ; Strömungsmechanik ; Numerisches Verfahren

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 online resource (466 pages) : , illustrations

Edition: Third edition.

ISBN: 0-08-099995-6 , 0-12-801172-6

Content: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques.

Note: Front Cover -- Computational Fluid Dynamics: Principles and Applications -- Copyright -- Contents -- Acknowledgments -- List of Symbols -- Abbreviations -- Chapter 1: Introduction -- Chapter 2: Governing Equations -- 2.1 The Flow and Its Mathematical Description -- 2.1.1 Finite control volume -- 2.2 Conservation Laws -- 2.2.1 The continuity equation -- 2.2.2 The momentum equation -- 2.2.3 The energy equation -- 2.3 Viscous Stresses -- 2.4 Complete System of the Navier-Stokes Equations -- 2.4.1 Formulation for a perfect gas -- 2.4.2 Formulation for a real gas -- 2.4.3 Simplifications to the Navier-Stokes equations -- Thin shear layer approximation -- Parabolized Navier-Stokes equations -- Euler equations -- References -- Chapter 3: Principles of Solution of the Governing Equations -- 3.1 Spatial Discretization -- 3.1.1 Finite-difference method -- 3.1.2 Finite-volume method -- 3.1.3 Finite-element method -- 3.1.4 Other discretization methods -- Spectral-element method -- Lattice Boltzmann method -- Gridless method -- 3.1.5 Central and upwind schemes -- Central schemes -- Upwind schemes -- Flux-vector splitting schemes -- Flux-difference splitting schemes -- TVD Schemes -- Fluctuation-splitting schemes -- Solution reconstruction -- First- and second-order schemes -- ENO/WENO Schemes -- Central versus upwind schemes -- Upwind schemes for real gas flows -- 3.2 Temporal Discretization -- 3.2.1 Explicit schemes -- 3.2.2 Implicit schemes -- 3.3 Turbulence Modeling -- 3.4 Initial and Boundary Conditions -- References -- Chapter 4: Structured Finite-Volume Schemes -- 4.1 Geometrical Quantities of a Control Volume -- 4.1.1 Two-dimensional case -- 4.1.2 Three-dimensional case -- 4.2 General Discretization Methodologies -- 4.2.1 Cell-centered scheme -- 4.2.2 Cell-vertex scheme: overlapping control volumes -- 4.2.3 Cell-vertex scheme: dual control volumes. , 4.2.4 Cell-centered versus cell-vertex schemes -- 4.3 Discretization of the Convective Fluxes -- 4.3.1 Central scheme with artificial dissipation -- Scalar dissipation scheme -- Matrix dissipation scheme -- 4.3.2 Flux-vector splitting schemes -- Van Leer's scheme -- AUSM -- CUSP scheme -- 4.3.3 Flux-difference splitting schemes -- Roe upwind scheme -- 4.3.4 Total variation diminishing schemes -- Upwind TVD scheme -- 4.3.5 Limiter functions -- Limiter functions for MUSCL interpolation -- MUSCL scheme with =0 -- MUSCL scheme with =1/3 -- Limiter for CUSP scheme -- Limiter for TVD scheme -- 4.4 Discretization of the Viscous Fluxes -- 4.4.1 Cell-centered scheme -- 4.4.2 Cell-vertex scheme -- References -- Chapter 5: Unstructured Finite-Volume Schemes -- 5.1 Geometrical Quantities of a Control Volume -- 5.1.1 Two-dimensional case -- Triangular element -- Quadrilateral element -- Element center -- 5.1.2 Three-dimensional case -- Triangular face -- Quadrilateral face -- Volume -- Cell centroid -- 5.2 General Discretization Methodologies -- 5.2.1 Cell-centered scheme -- 5.2.2 Median-dual cell-vertex scheme -- 5.2.3 Cell-centered versus median-dual scheme -- Accuracy -- Computational work -- Memory requirements -- Grid generation/adaptation -- 5.3 Discretization of the Convective Fluxes -- 5.3.1 Central scheme with artificial dissipation -- 5.3.2 Upwind schemes -- 5.3.3 Solution reconstruction -- Reconstruction based on MUSCL approach -- Piecewise linear reconstruction -- Linear reconstruction based on nodal weighting procedure -- Piecewise quadratic reconstruction -- 5.3.4 Evaluation of the gradients -- Green-Gauss approach -- Median-dual scheme -- Cell-centered scheme -- Mixed grids -- Least-squares approach -- 5.3.5 Limiter functions -- Limiter of Barth and Jespersen -- Venkatakrishnan's limiter -- 5.4 Discretization of the Viscous Fluxes. , 5.4.1 Element-based gradients -- Face-centered control volume -- Approximate Galerkin finite-element approach -- Average of nodal values -- 5.4.2 Average of gradients -- References -- Chapter 6: Temporal Discretization -- 6.1 Explicit Time-Stepping Schemes -- 6.1.1 Multistage schemes (Runge-Kutta) -- 6.1.2 Hybrid multistage schemes -- 6.1.3 Treatment of the source term -- 6.1.4 Determination of the maximum time step -- Time step on structured grids -- Euler equations -- Navier-Stokes equations -- Time step on unstructured grids -- Method 1 -- Method 2 -- 6.2 Implicit Time-Stepping Schemes -- 6.2.1 Matrix form of the implicit operator -- Implicit operator on structured grids -- Implicit operator on unstructured grids -- 6.2.2 Evaluation of the flux Jacobian -- Central scheme -- Flux-vector splitting scheme -- Flux-difference splitting scheme -- Viscous flows -- 6.2.3 Alternating direction implicit scheme -- 6.2.4 Lower-upper symmetric Gauss-Seidel scheme -- LU-SGS on structured grids -- LU-SGS on unstructured grids -- 6.2.5 Newton-Krylov method -- GMRES method -- Computation of the flux Jacobian -- Preconditioning -- Start-up problem -- 6.2.6 Implicit Runge-Kutta schemes -- 6.3 Methodologies for Unsteady Flows -- 6.3.1 Dual time-stepping for explicit multistage schemes -- 6.3.2 Dual time-stepping for implicit schemes -- References -- Chapter 7: Turbulence Modeling -- 7.1 Basic Equations of Turbulence -- 7.1.1 Reynolds averaging -- 7.1.2 Favre (mass) averaging -- 7.1.3 Reynolds-averaged Navier-Stokes equations -- 7.1.4 Favre- and Reynolds-averaged Navier-Stokes equations -- 7.1.5 Eddy-viscosity hypothesis -- 7.1.6 Non-linear eddy viscosity -- 7.1.7 Reynolds-stress transport equation -- 7.2 First-Order Closures -- 7.2.1 Spalart-Allmaras one-equation model -- Differential form -- Integral form -- Initial and boundary conditions. , 7.2.2 K - two-equation model -- Differential form -- Integral form -- Initial and boundary conditions -- Wall functions -- 7.2.3 SST two-equation model of Menter -- Differential form -- Boundary conditions -- 7.3 Large-Eddy Simulation -- 7.3.1 Spatial filtering -- 7.3.2 Filtered governing equations -- Incompressible Navier-Stokes equations -- Compressible Navier-Stokes equations -- 7.3.3 Subgrid-scale modeling -- Eddy-viscosity models -- Smagorinsky SGS model -- Dynamic SGS models -- 7.3.4 Wall models -- 7.3.5 Detached eddy simulation -- References -- Chapter 8: Boundary Conditions -- 8.1 Concept of Dummy Cells -- 8.2 Solid Wall -- 8.2.1 Inviscid flow -- Structured cell-centered scheme -- Structured cell-vertex scheme -- Unstructured cell-centered scheme -- Unstructured median-dual scheme -- 8.2.2 Viscous flow -- Cell-centered scheme -- Cell-vertex scheme -- 8.3 Far-Field -- 8.3.1 Concept of characteristic variables -- Supersonic inflow -- Supersonic outflow -- Subsonic inflow -- Subsonic outflow -- 8.3.2 Modifications for lifting bodies -- Vortex correction in 2D -- Vortex correction in 3D -- 8.4 Inlet/Outlet Boundary -- Subsonic inlet -- Subsonic outlet -- Supersonic inlet and outlet -- 8.5 Injection Boundary -- 8.6 Symmetry Plane -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- 8.7 Coordinate Cut -- 8.8 Periodic Boundaries -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- Rotational periodicity -- 8.9 Interface Between Grid Blocks -- 8.10 Flow Gradients at Boundaries of Unstructured Grids -- References -- Chapter 9: Acceleration Techniques -- 9.1 Local Time-Stepping -- 9.2 Enthalpy Damping -- 9.3 Residual Smoothing -- 9.3.1 Central IRS on structured grids -- 9.3.2 Central IRS on unstructured grids -- 9.3.3 Upwind IRS on structured grids -- 9.4 Multigrid -- 9.4.1 Basic multigrid cycle. , Transfer of the solution and residuals to the coarser grid -- Computation of a new solution on the coarse grid -- Solution interpolation from the coarse to the fine grid -- 9.4.2 Multigrid strategies -- Number of time steps -- Starting grid -- Accuracy of transfer operators -- 9.4.3 Implementation on structured grids -- Transfer operators for the cell-centered scheme -- Transfer operators for the cell-vertex scheme -- Upwind prolongation (cell-vertex scheme) -- 9.4.4 Implementation on unstructured grids -- Nonnested grids -- Topological methods -- Agglomeration multigrid method -- Generation of coarse grids by volume agglomeration -- Problems of agglomeration multigrid -- 9.5 Preconditioning for Low Mach Numbers -- 9.5.1 Derivation of preconditioned equations -- 9.5.2 Implementation -- 9.5.3 Form of the matrices -- Transformation matrices -- Preconditioning matrices -- Weiss and Smith preconditioner -- Eigenvalues of the preconditioned system -- Eigenvectors of the preconditioned system -- 9.6 Parallelization -- 9.6.1 MPI -- 9.6.2 OpenMP -- 9.6.3 CUDA -- 9.6.4 OpenCL -- References -- Chapter 10: Consistency, Accuracy, and Stability -- 10.1 Consistency Requirements -- 10.2 Accuracy of Discretization Scheme -- 10.3 Von Neumann Stability Analysis -- 10.3.1 Fourier symbol and amplification factor -- 10.3.2 Convection model equation -- Central scheme with artificial dissipation -- Upwind scheme -- 10.3.3 Convection-diffusion model equation -- 10.3.4 Explicit time-stepping -- Examples of Fourier symbols and amplification factors -- 10.3.5 Implicit time-stepping -- Examples of amplification factors -- 10.3.6 Derivation of the CFL condition -- CFL condition by von Neumann analysis -- References -- Chapter 11: Principles of Grid Generation -- 11.1 Structured Grids -- 11.1.1 C-, H-, and O-grid topology -- C-grid topology -- H-grid topology -- O-grid topology. , 11.1.2 Algebraic grid generation.

Language: English

UID:

Format: 1 online resource (466 pages) : , illustrations

Edition: Third edition.

ISBN: 0-08-099995-6 , 0-12-801172-6

Content: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques.

Note: Front Cover -- Computational Fluid Dynamics: Principles and Applications -- Copyright -- Contents -- Acknowledgments -- List of Symbols -- Abbreviations -- Chapter 1: Introduction -- Chapter 2: Governing Equations -- 2.1 The Flow and Its Mathematical Description -- 2.1.1 Finite control volume -- 2.2 Conservation Laws -- 2.2.1 The continuity equation -- 2.2.2 The momentum equation -- 2.2.3 The energy equation -- 2.3 Viscous Stresses -- 2.4 Complete System of the Navier-Stokes Equations -- 2.4.1 Formulation for a perfect gas -- 2.4.2 Formulation for a real gas -- 2.4.3 Simplifications to the Navier-Stokes equations -- Thin shear layer approximation -- Parabolized Navier-Stokes equations -- Euler equations -- References -- Chapter 3: Principles of Solution of the Governing Equations -- 3.1 Spatial Discretization -- 3.1.1 Finite-difference method -- 3.1.2 Finite-volume method -- 3.1.3 Finite-element method -- 3.1.4 Other discretization methods -- Spectral-element method -- Lattice Boltzmann method -- Gridless method -- 3.1.5 Central and upwind schemes -- Central schemes -- Upwind schemes -- Flux-vector splitting schemes -- Flux-difference splitting schemes -- TVD Schemes -- Fluctuation-splitting schemes -- Solution reconstruction -- First- and second-order schemes -- ENO/WENO Schemes -- Central versus upwind schemes -- Upwind schemes for real gas flows -- 3.2 Temporal Discretization -- 3.2.1 Explicit schemes -- 3.2.2 Implicit schemes -- 3.3 Turbulence Modeling -- 3.4 Initial and Boundary Conditions -- References -- Chapter 4: Structured Finite-Volume Schemes -- 4.1 Geometrical Quantities of a Control Volume -- 4.1.1 Two-dimensional case -- 4.1.2 Three-dimensional case -- 4.2 General Discretization Methodologies -- 4.2.1 Cell-centered scheme -- 4.2.2 Cell-vertex scheme: overlapping control volumes -- 4.2.3 Cell-vertex scheme: dual control volumes. , 4.2.4 Cell-centered versus cell-vertex schemes -- 4.3 Discretization of the Convective Fluxes -- 4.3.1 Central scheme with artificial dissipation -- Scalar dissipation scheme -- Matrix dissipation scheme -- 4.3.2 Flux-vector splitting schemes -- Van Leer's scheme -- AUSM -- CUSP scheme -- 4.3.3 Flux-difference splitting schemes -- Roe upwind scheme -- 4.3.4 Total variation diminishing schemes -- Upwind TVD scheme -- 4.3.5 Limiter functions -- Limiter functions for MUSCL interpolation -- MUSCL scheme with =0 -- MUSCL scheme with =1/3 -- Limiter for CUSP scheme -- Limiter for TVD scheme -- 4.4 Discretization of the Viscous Fluxes -- 4.4.1 Cell-centered scheme -- 4.4.2 Cell-vertex scheme -- References -- Chapter 5: Unstructured Finite-Volume Schemes -- 5.1 Geometrical Quantities of a Control Volume -- 5.1.1 Two-dimensional case -- Triangular element -- Quadrilateral element -- Element center -- 5.1.2 Three-dimensional case -- Triangular face -- Quadrilateral face -- Volume -- Cell centroid -- 5.2 General Discretization Methodologies -- 5.2.1 Cell-centered scheme -- 5.2.2 Median-dual cell-vertex scheme -- 5.2.3 Cell-centered versus median-dual scheme -- Accuracy -- Computational work -- Memory requirements -- Grid generation/adaptation -- 5.3 Discretization of the Convective Fluxes -- 5.3.1 Central scheme with artificial dissipation -- 5.3.2 Upwind schemes -- 5.3.3 Solution reconstruction -- Reconstruction based on MUSCL approach -- Piecewise linear reconstruction -- Linear reconstruction based on nodal weighting procedure -- Piecewise quadratic reconstruction -- 5.3.4 Evaluation of the gradients -- Green-Gauss approach -- Median-dual scheme -- Cell-centered scheme -- Mixed grids -- Least-squares approach -- 5.3.5 Limiter functions -- Limiter of Barth and Jespersen -- Venkatakrishnan's limiter -- 5.4 Discretization of the Viscous Fluxes. , 5.4.1 Element-based gradients -- Face-centered control volume -- Approximate Galerkin finite-element approach -- Average of nodal values -- 5.4.2 Average of gradients -- References -- Chapter 6: Temporal Discretization -- 6.1 Explicit Time-Stepping Schemes -- 6.1.1 Multistage schemes (Runge-Kutta) -- 6.1.2 Hybrid multistage schemes -- 6.1.3 Treatment of the source term -- 6.1.4 Determination of the maximum time step -- Time step on structured grids -- Euler equations -- Navier-Stokes equations -- Time step on unstructured grids -- Method 1 -- Method 2 -- 6.2 Implicit Time-Stepping Schemes -- 6.2.1 Matrix form of the implicit operator -- Implicit operator on structured grids -- Implicit operator on unstructured grids -- 6.2.2 Evaluation of the flux Jacobian -- Central scheme -- Flux-vector splitting scheme -- Flux-difference splitting scheme -- Viscous flows -- 6.2.3 Alternating direction implicit scheme -- 6.2.4 Lower-upper symmetric Gauss-Seidel scheme -- LU-SGS on structured grids -- LU-SGS on unstructured grids -- 6.2.5 Newton-Krylov method -- GMRES method -- Computation of the flux Jacobian -- Preconditioning -- Start-up problem -- 6.2.6 Implicit Runge-Kutta schemes -- 6.3 Methodologies for Unsteady Flows -- 6.3.1 Dual time-stepping for explicit multistage schemes -- 6.3.2 Dual time-stepping for implicit schemes -- References -- Chapter 7: Turbulence Modeling -- 7.1 Basic Equations of Turbulence -- 7.1.1 Reynolds averaging -- 7.1.2 Favre (mass) averaging -- 7.1.3 Reynolds-averaged Navier-Stokes equations -- 7.1.4 Favre- and Reynolds-averaged Navier-Stokes equations -- 7.1.5 Eddy-viscosity hypothesis -- 7.1.6 Non-linear eddy viscosity -- 7.1.7 Reynolds-stress transport equation -- 7.2 First-Order Closures -- 7.2.1 Spalart-Allmaras one-equation model -- Differential form -- Integral form -- Initial and boundary conditions. , 7.2.2 K - two-equation model -- Differential form -- Integral form -- Initial and boundary conditions -- Wall functions -- 7.2.3 SST two-equation model of Menter -- Differential form -- Boundary conditions -- 7.3 Large-Eddy Simulation -- 7.3.1 Spatial filtering -- 7.3.2 Filtered governing equations -- Incompressible Navier-Stokes equations -- Compressible Navier-Stokes equations -- 7.3.3 Subgrid-scale modeling -- Eddy-viscosity models -- Smagorinsky SGS model -- Dynamic SGS models -- 7.3.4 Wall models -- 7.3.5 Detached eddy simulation -- References -- Chapter 8: Boundary Conditions -- 8.1 Concept of Dummy Cells -- 8.2 Solid Wall -- 8.2.1 Inviscid flow -- Structured cell-centered scheme -- Structured cell-vertex scheme -- Unstructured cell-centered scheme -- Unstructured median-dual scheme -- 8.2.2 Viscous flow -- Cell-centered scheme -- Cell-vertex scheme -- 8.3 Far-Field -- 8.3.1 Concept of characteristic variables -- Supersonic inflow -- Supersonic outflow -- Subsonic inflow -- Subsonic outflow -- 8.3.2 Modifications for lifting bodies -- Vortex correction in 2D -- Vortex correction in 3D -- 8.4 Inlet/Outlet Boundary -- Subsonic inlet -- Subsonic outlet -- Supersonic inlet and outlet -- 8.5 Injection Boundary -- 8.6 Symmetry Plane -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- 8.7 Coordinate Cut -- 8.8 Periodic Boundaries -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- Rotational periodicity -- 8.9 Interface Between Grid Blocks -- 8.10 Flow Gradients at Boundaries of Unstructured Grids -- References -- Chapter 9: Acceleration Techniques -- 9.1 Local Time-Stepping -- 9.2 Enthalpy Damping -- 9.3 Residual Smoothing -- 9.3.1 Central IRS on structured grids -- 9.3.2 Central IRS on unstructured grids -- 9.3.3 Upwind IRS on structured grids -- 9.4 Multigrid -- 9.4.1 Basic multigrid cycle. , Transfer of the solution and residuals to the coarser grid -- Computation of a new solution on the coarse grid -- Solution interpolation from the coarse to the fine grid -- 9.4.2 Multigrid strategies -- Number of time steps -- Starting grid -- Accuracy of transfer operators -- 9.4.3 Implementation on structured grids -- Transfer operators for the cell-centered scheme -- Transfer operators for the cell-vertex scheme -- Upwind prolongation (cell-vertex scheme) -- 9.4.4 Implementation on unstructured grids -- Nonnested grids -- Topological methods -- Agglomeration multigrid method -- Generation of coarse grids by volume agglomeration -- Problems of agglomeration multigrid -- 9.5 Preconditioning for Low Mach Numbers -- 9.5.1 Derivation of preconditioned equations -- 9.5.2 Implementation -- 9.5.3 Form of the matrices -- Transformation matrices -- Preconditioning matrices -- Weiss and Smith preconditioner -- Eigenvalues of the preconditioned system -- Eigenvectors of the preconditioned system -- 9.6 Parallelization -- 9.6.1 MPI -- 9.6.2 OpenMP -- 9.6.3 CUDA -- 9.6.4 OpenCL -- References -- Chapter 10: Consistency, Accuracy, and Stability -- 10.1 Consistency Requirements -- 10.2 Accuracy of Discretization Scheme -- 10.3 Von Neumann Stability Analysis -- 10.3.1 Fourier symbol and amplification factor -- 10.3.2 Convection model equation -- Central scheme with artificial dissipation -- Upwind scheme -- 10.3.3 Convection-diffusion model equation -- 10.3.4 Explicit time-stepping -- Examples of Fourier symbols and amplification factors -- 10.3.5 Implicit time-stepping -- Examples of amplification factors -- 10.3.6 Derivation of the CFL condition -- CFL condition by von Neumann analysis -- References -- Chapter 11: Principles of Grid Generation -- 11.1 Structured Grids -- 11.1.1 C-, H-, and O-grid topology -- C-grid topology -- H-grid topology -- O-grid topology. , 11.1.2 Algebraic grid generation.

Language: English

UID:

Format: 1 online resource (466 pages) : , illustrations

Edition: Third edition.

ISBN: 0-08-099995-6 , 0-12-801172-6

Content: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques.

Note: Front Cover -- Computational Fluid Dynamics: Principles and Applications -- Copyright -- Contents -- Acknowledgments -- List of Symbols -- Abbreviations -- Chapter 1: Introduction -- Chapter 2: Governing Equations -- 2.1 The Flow and Its Mathematical Description -- 2.1.1 Finite control volume -- 2.2 Conservation Laws -- 2.2.1 The continuity equation -- 2.2.2 The momentum equation -- 2.2.3 The energy equation -- 2.3 Viscous Stresses -- 2.4 Complete System of the Navier-Stokes Equations -- 2.4.1 Formulation for a perfect gas -- 2.4.2 Formulation for a real gas -- 2.4.3 Simplifications to the Navier-Stokes equations -- Thin shear layer approximation -- Parabolized Navier-Stokes equations -- Euler equations -- References -- Chapter 3: Principles of Solution of the Governing Equations -- 3.1 Spatial Discretization -- 3.1.1 Finite-difference method -- 3.1.2 Finite-volume method -- 3.1.3 Finite-element method -- 3.1.4 Other discretization methods -- Spectral-element method -- Lattice Boltzmann method -- Gridless method -- 3.1.5 Central and upwind schemes -- Central schemes -- Upwind schemes -- Flux-vector splitting schemes -- Flux-difference splitting schemes -- TVD Schemes -- Fluctuation-splitting schemes -- Solution reconstruction -- First- and second-order schemes -- ENO/WENO Schemes -- Central versus upwind schemes -- Upwind schemes for real gas flows -- 3.2 Temporal Discretization -- 3.2.1 Explicit schemes -- 3.2.2 Implicit schemes -- 3.3 Turbulence Modeling -- 3.4 Initial and Boundary Conditions -- References -- Chapter 4: Structured Finite-Volume Schemes -- 4.1 Geometrical Quantities of a Control Volume -- 4.1.1 Two-dimensional case -- 4.1.2 Three-dimensional case -- 4.2 General Discretization Methodologies -- 4.2.1 Cell-centered scheme -- 4.2.2 Cell-vertex scheme: overlapping control volumes -- 4.2.3 Cell-vertex scheme: dual control volumes. , 4.2.4 Cell-centered versus cell-vertex schemes -- 4.3 Discretization of the Convective Fluxes -- 4.3.1 Central scheme with artificial dissipation -- Scalar dissipation scheme -- Matrix dissipation scheme -- 4.3.2 Flux-vector splitting schemes -- Van Leer's scheme -- AUSM -- CUSP scheme -- 4.3.3 Flux-difference splitting schemes -- Roe upwind scheme -- 4.3.4 Total variation diminishing schemes -- Upwind TVD scheme -- 4.3.5 Limiter functions -- Limiter functions for MUSCL interpolation -- MUSCL scheme with =0 -- MUSCL scheme with =1/3 -- Limiter for CUSP scheme -- Limiter for TVD scheme -- 4.4 Discretization of the Viscous Fluxes -- 4.4.1 Cell-centered scheme -- 4.4.2 Cell-vertex scheme -- References -- Chapter 5: Unstructured Finite-Volume Schemes -- 5.1 Geometrical Quantities of a Control Volume -- 5.1.1 Two-dimensional case -- Triangular element -- Quadrilateral element -- Element center -- 5.1.2 Three-dimensional case -- Triangular face -- Quadrilateral face -- Volume -- Cell centroid -- 5.2 General Discretization Methodologies -- 5.2.1 Cell-centered scheme -- 5.2.2 Median-dual cell-vertex scheme -- 5.2.3 Cell-centered versus median-dual scheme -- Accuracy -- Computational work -- Memory requirements -- Grid generation/adaptation -- 5.3 Discretization of the Convective Fluxes -- 5.3.1 Central scheme with artificial dissipation -- 5.3.2 Upwind schemes -- 5.3.3 Solution reconstruction -- Reconstruction based on MUSCL approach -- Piecewise linear reconstruction -- Linear reconstruction based on nodal weighting procedure -- Piecewise quadratic reconstruction -- 5.3.4 Evaluation of the gradients -- Green-Gauss approach -- Median-dual scheme -- Cell-centered scheme -- Mixed grids -- Least-squares approach -- 5.3.5 Limiter functions -- Limiter of Barth and Jespersen -- Venkatakrishnan's limiter -- 5.4 Discretization of the Viscous Fluxes. , 5.4.1 Element-based gradients -- Face-centered control volume -- Approximate Galerkin finite-element approach -- Average of nodal values -- 5.4.2 Average of gradients -- References -- Chapter 6: Temporal Discretization -- 6.1 Explicit Time-Stepping Schemes -- 6.1.1 Multistage schemes (Runge-Kutta) -- 6.1.2 Hybrid multistage schemes -- 6.1.3 Treatment of the source term -- 6.1.4 Determination of the maximum time step -- Time step on structured grids -- Euler equations -- Navier-Stokes equations -- Time step on unstructured grids -- Method 1 -- Method 2 -- 6.2 Implicit Time-Stepping Schemes -- 6.2.1 Matrix form of the implicit operator -- Implicit operator on structured grids -- Implicit operator on unstructured grids -- 6.2.2 Evaluation of the flux Jacobian -- Central scheme -- Flux-vector splitting scheme -- Flux-difference splitting scheme -- Viscous flows -- 6.2.3 Alternating direction implicit scheme -- 6.2.4 Lower-upper symmetric Gauss-Seidel scheme -- LU-SGS on structured grids -- LU-SGS on unstructured grids -- 6.2.5 Newton-Krylov method -- GMRES method -- Computation of the flux Jacobian -- Preconditioning -- Start-up problem -- 6.2.6 Implicit Runge-Kutta schemes -- 6.3 Methodologies for Unsteady Flows -- 6.3.1 Dual time-stepping for explicit multistage schemes -- 6.3.2 Dual time-stepping for implicit schemes -- References -- Chapter 7: Turbulence Modeling -- 7.1 Basic Equations of Turbulence -- 7.1.1 Reynolds averaging -- 7.1.2 Favre (mass) averaging -- 7.1.3 Reynolds-averaged Navier-Stokes equations -- 7.1.4 Favre- and Reynolds-averaged Navier-Stokes equations -- 7.1.5 Eddy-viscosity hypothesis -- 7.1.6 Non-linear eddy viscosity -- 7.1.7 Reynolds-stress transport equation -- 7.2 First-Order Closures -- 7.2.1 Spalart-Allmaras one-equation model -- Differential form -- Integral form -- Initial and boundary conditions. , 7.2.2 K - two-equation model -- Differential form -- Integral form -- Initial and boundary conditions -- Wall functions -- 7.2.3 SST two-equation model of Menter -- Differential form -- Boundary conditions -- 7.3 Large-Eddy Simulation -- 7.3.1 Spatial filtering -- 7.3.2 Filtered governing equations -- Incompressible Navier-Stokes equations -- Compressible Navier-Stokes equations -- 7.3.3 Subgrid-scale modeling -- Eddy-viscosity models -- Smagorinsky SGS model -- Dynamic SGS models -- 7.3.4 Wall models -- 7.3.5 Detached eddy simulation -- References -- Chapter 8: Boundary Conditions -- 8.1 Concept of Dummy Cells -- 8.2 Solid Wall -- 8.2.1 Inviscid flow -- Structured cell-centered scheme -- Structured cell-vertex scheme -- Unstructured cell-centered scheme -- Unstructured median-dual scheme -- 8.2.2 Viscous flow -- Cell-centered scheme -- Cell-vertex scheme -- 8.3 Far-Field -- 8.3.1 Concept of characteristic variables -- Supersonic inflow -- Supersonic outflow -- Subsonic inflow -- Subsonic outflow -- 8.3.2 Modifications for lifting bodies -- Vortex correction in 2D -- Vortex correction in 3D -- 8.4 Inlet/Outlet Boundary -- Subsonic inlet -- Subsonic outlet -- Supersonic inlet and outlet -- 8.5 Injection Boundary -- 8.6 Symmetry Plane -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- 8.7 Coordinate Cut -- 8.8 Periodic Boundaries -- Cell-centered scheme -- Cell-vertex scheme (dual control volume) -- Rotational periodicity -- 8.9 Interface Between Grid Blocks -- 8.10 Flow Gradients at Boundaries of Unstructured Grids -- References -- Chapter 9: Acceleration Techniques -- 9.1 Local Time-Stepping -- 9.2 Enthalpy Damping -- 9.3 Residual Smoothing -- 9.3.1 Central IRS on structured grids -- 9.3.2 Central IRS on unstructured grids -- 9.3.3 Upwind IRS on structured grids -- 9.4 Multigrid -- 9.4.1 Basic multigrid cycle. , Transfer of the solution and residuals to the coarser grid -- Computation of a new solution on the coarse grid -- Solution interpolation from the coarse to the fine grid -- 9.4.2 Multigrid strategies -- Number of time steps -- Starting grid -- Accuracy of transfer operators -- 9.4.3 Implementation on structured grids -- Transfer operators for the cell-centered scheme -- Transfer operators for the cell-vertex scheme -- Upwind prolongation (cell-vertex scheme) -- 9.4.4 Implementation on unstructured grids -- Nonnested grids -- Topological methods -- Agglomeration multigrid method -- Generation of coarse grids by volume agglomeration -- Problems of agglomeration multigrid -- 9.5 Preconditioning for Low Mach Numbers -- 9.5.1 Derivation of preconditioned equations -- 9.5.2 Implementation -- 9.5.3 Form of the matrices -- Transformation matrices -- Preconditioning matrices -- Weiss and Smith preconditioner -- Eigenvalues of the preconditioned system -- Eigenvectors of the preconditioned system -- 9.6 Parallelization -- 9.6.1 MPI -- 9.6.2 OpenMP -- 9.6.3 CUDA -- 9.6.4 OpenCL -- References -- Chapter 10: Consistency, Accuracy, and Stability -- 10.1 Consistency Requirements -- 10.2 Accuracy of Discretization Scheme -- 10.3 Von Neumann Stability Analysis -- 10.3.1 Fourier symbol and amplification factor -- 10.3.2 Convection model equation -- Central scheme with artificial dissipation -- Upwind scheme -- 10.3.3 Convection-diffusion model equation -- 10.3.4 Explicit time-stepping -- Examples of Fourier symbols and amplification factors -- 10.3.5 Implicit time-stepping -- Examples of amplification factors -- 10.3.6 Derivation of the CFL condition -- CFL condition by von Neumann analysis -- References -- Chapter 11: Principles of Grid Generation -- 11.1 Structured Grids -- 11.1.1 C-, H-, and O-grid topology -- C-grid topology -- H-grid topology -- O-grid topology. , 11.1.2 Algebraic grid generation.

Language: English