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High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta [[electronic resource]]
High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta [[electronic resource]]
Autore Sengupta Tapan Kumar <1955->
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xix, 569 pages) : digital, PDF file(s)
Disciplina 532/.050285
Soggetto topico Fluid dynamics - Data processing
Wave mechanics - Data processing
Spectrum analysis - Data processing
ISBN 1-107-05783-3
1-107-05456-7
1-107-05907-0
1-107-05561-X
1-139-15182-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Machine generated contents note: ch. 1 Basic Ideas of Scientific Computing -- 1.1.Overview on Scientific Computing -- 1.2.Major Milestones in Electronic Computing -- 1.3.Supercomputing and High Performance Computing -- 1.3.1.Parallel and cluster computing -- 1.3.2.Algorithmic issues of HPC -- 1.4.Computational Fluid Mechanics -- 1.5.Role of Computational Fluid Mechanics -- ch. 2 Governing Equations in Fluid Mechanics -- 2.1.Introduction -- 2.2.Basic Equations of Fluid Mechanics -- 2.2.1.Finite control volume -- 2.2.2.Infinitesimal fluid element -- 2.2.3.Substantive derivative -- 2.3.Equation of Continuity -- 2.4.Momentum Conservation Equation -- 2.5.Energy Conservation Equation -- 2.6.Alternate Forms of Energy Equation -- 2.7.The Energy Equation in Conservation Form -- 2.8.Notes on Governing Equations -- 2.9.Strong Conservation and Weak Conservation Forms -- 2.10.Boundary and Initial Conditions (Auxiliary Conditions) -- 2.11.Equations of Motion in Non-Inertial Frame -- 2.12.Equations of Motion in Terms of Derived Variables -- 2.13.Vorticity-Vector Potential Formulation -- 2.14.Pressure Poisson Equation -- 2.15.Comparison of Different Formulations -- 2.16.Other Forms of Navier-Stokes Equation -- ch. 3 Classification of Quasi-Linear Partial Differential Equations -- 3.1.Introduction -- 3.2.Classification of Partial Differential Equations -- 3.3.Relationship of Numerical Solution Procedure and Equation Type -- 3.4.Nature of Well-Posed Problems -- 3.5.Non-Dimensional Form of Equations -- ch. 4 Waves and Space-Time Dependence in Computing -- 4.1.Introduction -- 4.2.The Wave Equation -- 4.2.1.Plane waves -- 4.2.2.Three-dimensional axisymmetric wave -- 4.2.3.Doppler shift -- 4.2.4.Surface gravity waves -- 4.3.Deep and Shallow Water Waves -- 4.4.Group Velocity and Energy Flux -- 4.4.1.Physical and computational implications of group velocity -- 4.4.2.Wave-packets and their propagation -- 4.4.3.Waves over layer of constant depth -- 4.4.4.Waves over layer of variable depth H(x) -- 4.4.5.Wave refraction in shallow waters -- 4.4.6.Finite amplitude waves of unchanging form in dispersive medium -- 4.5.Internal Waves at Fluid Interface: Rayleigh-Taylor Problem -- 4.5.1.Internal and surface waves in finite over an infinite deep layer of fluid -- 4.5.2.Barotropic or surface mode -- 4.5.3.Baroclinic or internal mode -- 4.5.4.Rotating shallow water equation and wave dynamics -- 4.6.Shallow Water Equation (SWE) -- 4.6.1.Various frequency regimes of SWE -- 4.7.Additional Issues of Computing: Space-Time Resolution of Flows -- 4.7.1.Spatial scales in turbulent flows -- 4.8.Two- and Three-Dimensional DNS -- 4.9.Temporal Scales in Turbulent Flows -- 4.10.Computing Time-Averaged and Unsteady Flows -- ch. 5 Spatial and Temporal Discretizations of Partial Differential Equations -- 5.1.Introduction -- 5.2.Discretization of Differential Operators -- 5.2.1.Functional representation by the Taylor series -- 5.2.2.Polynomial representation of function -- 5.3.Discretization in Non-Uniform Grids -- 5.4.Higher Order Representation of Derivatives Using Operators -- 5.5.Higher Order Upwind Differences -- 5.5.1.Symmetric stencil for higher derivatives -- 5.6.Numerical Errors -- 5.7.Time Integration -- 5.7.1.Single-step methods -- 5.7.2.Single-step multi-stage methods -- 5.7.3.Runge-Kutta methods -- 5.7.4.Multi-step time integration schemes -- ch. 6 Solution Methods for Parabolic Partial Differential Equations -- 6.1.Introduction -- 6.2.Theoretical Analysis of the Heat Equation -- 6.3.A Classical Algorithm for Solution of the Heat Equation -- 6.4.Spectral Analysis of Numerical Methods -- 6.4.1.A higher order method or Milne's method -- 6.5.Treating Derivative Boundary Condition -- 6.6.Stability, Accuracy and Consistency of Numerical Methods -- 6.6.1.Richardson's method -- 6.6.2.Du Fort -- Frankel method -- 6.7.Implicit Methods -- 6.8.Spectral Stability Analysis of Implicit Methods -- Appendix I -- ch. 7 Solution Methods for Elliptic Partial Differential Equations -- 7.1.Introduction -- 7.2.Jacobi or Richardson Iteration -- 7.3.Interpretation of Classical Iterations -- 7.4.Different Point and Line Iterative Methods -- 7.4.1.Gauss-Seidel point iterative method -- 7.4.2.Line Jacobi method -- 7.4.3.Explanation of line iteration methods -- 7.5.Analysis of Iterative Methods -- 7.6.Convergence Theorem for Stationary Linear Iteration -- 7.7.Relaxation Methods -- 7.8.Efficiency of Iterative Methods and Rate of Convergence -- 7.8.1.Method of acceleration due to Lyusternik -- 7.9.Alternate Direction Implicit (ADI) Method -- 7.9.1.Analysis of ADI method -- 7.9.2.Choice of acceleration parameters -- 7.9.3.Estimates of maximum and minimum eigenvalues -- 7.9.4.Explanatory notes on ADI and other variant methods -- 7.10.Method of Fractional Steps -- 7.11.Multi-Grid Methods -- 7.11.1.Two-Grid method -- 7.11.2.Multi-Grid method -- 7.11.3.Other classifications of multi-grid method -- ch. 8 Solution of Hyperbolic PDEs: Signal and Error Propagation -- 8.1.Introduction -- 8.2.Classical Methods of Solving Hyperbolic Equations -- 8.2.1.Explicit methods -- 8.3.Implicit Methods -- 8.4.General Characteristics of Various Methods for Linear Problems -- 8.5.Non-linear Hyperbolic Problems -- 8.6.Error Dynamics: Beyond von Neumann Analysis -- 8.6.1.Dispersion error and its quantification -- 8.7.Role of Group Velocity and Focussing -- 8.7.1.Focussing phenomenon -- ch. 9 Curvilinear Coordinate and Grid Generation -- 9.1.Introduction -- 9.2.Generalized Curvilinear Scheme -- 9.3.Reciprocal or Dual Base Vectors -- 9.4.Geometric Interpretation of Metrics -- 9.5.Orthogonal Grid System -- 9.6.Generalized Coordinate Transformation -- 9.7.Equations for the Metrics -- 9.8.Navier-Stokes Equation in the Transformed Plane -- 9.9.Linearization of Fluxes -- 9.10.Thin Layer Navier-Stokes Equation -- 9.11.Grid Generation -- 9.12.Types of Grid -- 9.13.Grid Generation Methods -- 9.14.Algebraic Grid Generation Method -- 9.14.1.One-dimensional stretching functions -- 9.15.Grid Generation by Solving Partial Differential Equations -- 9.16.Elliptic Grid Generators -- 9.17.Hyperbolic Grid Generation Method -- 9.18.Orthogonal Grid Generation for Navier-Stokes Computations -- 9.19.Coordinate Transformations and Governing Equations in Orthogonal System -- 9.19.1.Gradient operator -- 9.19.2.Divergence operator -- 9.19.3.The Laplacian operator -- 9.19.4.The curl operator -- 9.19.5.The line integral -- 9.19.6.The surface integral -- 9.19.7.The volume integral -- 9.20.The Gradient and Laplacian of Scalar Function -- 9.21.Vector Operators of a Vector Function -- 9.22.Plane Polar Coordinates -- 9.23.Navier-Stokes Equation in Orthogonal Formulation -- 9.24.Improved Orthogonal Grid Generation Method for Cambered Airfoils -- 9.24.1.Orthogonal grid generation for GA(W)-1 airfoil -- 9.24.2.Orthogonal grid generation for an airfoil with roughness element -- 9.24.3.Solutions of Navier-Stokes equation for flow past SHM-1 airfoil -- 9.24.4.Compressible flow past NACA 0012 airfoil -- 9.25.Governing Euler Equation, Auxiliary Conditions, Numerical Methods and Results -- 9.26.Flow Field Calculation Using Overset or Chimera Grid Technique -- ch.
10 Spectral Analysis of Numerical Schemes and Aliasing Error -- 10.1.Introduction -- 10.2.Spatial Discretization of First Derivatives -- 10.2.1.Second order central differencing (CD2) scheme -- 10.3.Discrete Computing and Nyquist Criterion -- 10.4.Spectral Accuracy of Differentiation -- 10.5.Spectral Analysis of Fourth Order Central Difference Scheme -- 10.6.Role of Upwinding -- 10.6.1.First order upwind scheme (UD1) -- 10.6.2.Third order upwind scheme (UD3) -- 10.7.Numerical Stability and Concept of Feedback -- 10.8.Spectral Stability Analysis -- 10.9.High Accuracy Schemes for Spatial Derivatives -- 10.10.Temporal Discretization Schemes -- 10.10.1.Euler time integration scheme -- 10.10.2.Four-stage Runge-Kutta (RK4) method -- 10.11.Multi-Time Level Discretization Schemes -- 10.11.1.Mid-point leapfrog scheme -- 10.11.2.Second order Adams-Bashforth scheme -- 10.12.Aliasing Error -- 10.12.1.Why aliasing error is important? -- 10.12.2.Estimation of aliased component -- 10.13.Numerical Estimates of Aliasing Error -- 10.14.Controlling Aliasing Error -- 10.14.1.Aliasing removal by zero padding -- 10.14.2.Aliasing removal by phase shifts and grid-staggering -- ch. 11 Higher Accuracy Methods -- 11.1.Introduction -- 11.2.The General Compact Schemes -- 11.2.1.Approximating first derivatives by central scheme -- 11.3.Method for Solving Periodic Tridiagonal Matrix Equation -- 11.4.An Example of a Sixth Order Scheme -- 11.5.Order of Approximation versus Resolution -- 11.6.Optimization Problem Associated with Discrete Evaluation of First Derivatives -- 11.7.An Optimized Compact Scheme For First Derivative by Grid Search Method -- 11.8.Upwind Compact Schemes -- 11.9.Compact Schemes with Improved Numerical Properties -- 11.9.1.OUCS1 scheme -- 11.9.2.OUCS2 scheme -- 11.9.3.OUCS3 scheme -- 11.9.4.OUCS4 scheme -- 11.10.Approximating Second Derivatives -- 11.11.Optimization Problem for Evaluation of the Second Derivatives -- 11.12.Solution of One-Dimensional Convection Equation -- 11.13.Symmetrized Compact Difference Schemes -- 11.13.1.High accuracy symmetrized compact scheme -- 11.13.2.Solving bidirectional wave equation -- 11.13.3.Transitional channel flow -- 11.13.3.1.Establishment of equilibrium flow -- 11.13.3.2.Receptivity of channel flow to convecting single viscous vortex -- 11.13.4.Transitional channel flow created by vortex street -- 11.14.Combined Compact Difference (CCD) Schemes -- 11.14.1.A new combined compact difference (NCCD) scheme -- 11.14.2.Solving the Stommel Ocean Model problem -- 11.14.3.Operational aspects of the CCD schemes -- 11.14.4.Calibrating NCCD method to solve Navier-Stokes equation for 2D lid-driven cavity problem -- 11.15.Diffusion Discretization and Dealiasing Properties of Compact Schemes -- 11.15.1.Dynamics and aliasing in square LDC problem --
Record Nr. UNINA-9910463471803321
Sengupta Tapan Kumar <1955->  
Cambridge : , : Cambridge University Press, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta [[electronic resource]]
High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta [[electronic resource]]
Autore Sengupta Tapan Kumar <1955->
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xix, 569 pages) : digital, PDF file(s)
Disciplina 532/.050285
Soggetto topico Fluid dynamics - Data processing
Wave mechanics - Data processing
Spectrum analysis - Data processing
ISBN 1-107-06965-3
1-107-05783-3
1-107-05456-7
1-107-05907-0
1-107-05561-X
1-139-15182-7
Classificazione COM000000
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Machine generated contents note: ch. 1 Basic Ideas of Scientific Computing -- 1.1.Overview on Scientific Computing -- 1.2.Major Milestones in Electronic Computing -- 1.3.Supercomputing and High Performance Computing -- 1.3.1.Parallel and cluster computing -- 1.3.2.Algorithmic issues of HPC -- 1.4.Computational Fluid Mechanics -- 1.5.Role of Computational Fluid Mechanics -- ch. 2 Governing Equations in Fluid Mechanics -- 2.1.Introduction -- 2.2.Basic Equations of Fluid Mechanics -- 2.2.1.Finite control volume -- 2.2.2.Infinitesimal fluid element -- 2.2.3.Substantive derivative -- 2.3.Equation of Continuity -- 2.4.Momentum Conservation Equation -- 2.5.Energy Conservation Equation -- 2.6.Alternate Forms of Energy Equation -- 2.7.The Energy Equation in Conservation Form -- 2.8.Notes on Governing Equations -- 2.9.Strong Conservation and Weak Conservation Forms -- 2.10.Boundary and Initial Conditions (Auxiliary Conditions) -- 2.11.Equations of Motion in Non-Inertial Frame -- 2.12.Equations of Motion in Terms of Derived Variables -- 2.13.Vorticity-Vector Potential Formulation -- 2.14.Pressure Poisson Equation -- 2.15.Comparison of Different Formulations -- 2.16.Other Forms of Navier-Stokes Equation -- ch. 3 Classification of Quasi-Linear Partial Differential Equations -- 3.1.Introduction -- 3.2.Classification of Partial Differential Equations -- 3.3.Relationship of Numerical Solution Procedure and Equation Type -- 3.4.Nature of Well-Posed Problems -- 3.5.Non-Dimensional Form of Equations -- ch. 4 Waves and Space-Time Dependence in Computing -- 4.1.Introduction -- 4.2.The Wave Equation -- 4.2.1.Plane waves -- 4.2.2.Three-dimensional axisymmetric wave -- 4.2.3.Doppler shift -- 4.2.4.Surface gravity waves -- 4.3.Deep and Shallow Water Waves -- 4.4.Group Velocity and Energy Flux -- 4.4.1.Physical and computational implications of group velocity -- 4.4.2.Wave-packets and their propagation -- 4.4.3.Waves over layer of constant depth -- 4.4.4.Waves over layer of variable depth H(x) -- 4.4.5.Wave refraction in shallow waters -- 4.4.6.Finite amplitude waves of unchanging form in dispersive medium -- 4.5.Internal Waves at Fluid Interface: Rayleigh-Taylor Problem -- 4.5.1.Internal and surface waves in finite over an infinite deep layer of fluid -- 4.5.2.Barotropic or surface mode -- 4.5.3.Baroclinic or internal mode -- 4.5.4.Rotating shallow water equation and wave dynamics -- 4.6.Shallow Water Equation (SWE) -- 4.6.1.Various frequency regimes of SWE -- 4.7.Additional Issues of Computing: Space-Time Resolution of Flows -- 4.7.1.Spatial scales in turbulent flows -- 4.8.Two- and Three-Dimensional DNS -- 4.9.Temporal Scales in Turbulent Flows -- 4.10.Computing Time-Averaged and Unsteady Flows -- ch. 5 Spatial and Temporal Discretizations of Partial Differential Equations -- 5.1.Introduction -- 5.2.Discretization of Differential Operators -- 5.2.1.Functional representation by the Taylor series -- 5.2.2.Polynomial representation of function -- 5.3.Discretization in Non-Uniform Grids -- 5.4.Higher Order Representation of Derivatives Using Operators -- 5.5.Higher Order Upwind Differences -- 5.5.1.Symmetric stencil for higher derivatives -- 5.6.Numerical Errors -- 5.7.Time Integration -- 5.7.1.Single-step methods -- 5.7.2.Single-step multi-stage methods -- 5.7.3.Runge-Kutta methods -- 5.7.4.Multi-step time integration schemes -- ch. 6 Solution Methods for Parabolic Partial Differential Equations -- 6.1.Introduction -- 6.2.Theoretical Analysis of the Heat Equation -- 6.3.A Classical Algorithm for Solution of the Heat Equation -- 6.4.Spectral Analysis of Numerical Methods -- 6.4.1.A higher order method or Milne's method -- 6.5.Treating Derivative Boundary Condition -- 6.6.Stability, Accuracy and Consistency of Numerical Methods -- 6.6.1.Richardson's method -- 6.6.2.Du Fort -- Frankel method -- 6.7.Implicit Methods -- 6.8.Spectral Stability Analysis of Implicit Methods -- Appendix I -- ch. 7 Solution Methods for Elliptic Partial Differential Equations -- 7.1.Introduction -- 7.2.Jacobi or Richardson Iteration -- 7.3.Interpretation of Classical Iterations -- 7.4.Different Point and Line Iterative Methods -- 7.4.1.Gauss-Seidel point iterative method -- 7.4.2.Line Jacobi method -- 7.4.3.Explanation of line iteration methods -- 7.5.Analysis of Iterative Methods -- 7.6.Convergence Theorem for Stationary Linear Iteration -- 7.7.Relaxation Methods -- 7.8.Efficiency of Iterative Methods and Rate of Convergence -- 7.8.1.Method of acceleration due to Lyusternik -- 7.9.Alternate Direction Implicit (ADI) Method -- 7.9.1.Analysis of ADI method -- 7.9.2.Choice of acceleration parameters -- 7.9.3.Estimates of maximum and minimum eigenvalues -- 7.9.4.Explanatory notes on ADI and other variant methods -- 7.10.Method of Fractional Steps -- 7.11.Multi-Grid Methods -- 7.11.1.Two-Grid method -- 7.11.2.Multi-Grid method -- 7.11.3.Other classifications of multi-grid method -- ch. 8 Solution of Hyperbolic PDEs: Signal and Error Propagation -- 8.1.Introduction -- 8.2.Classical Methods of Solving Hyperbolic Equations -- 8.2.1.Explicit methods -- 8.3.Implicit Methods -- 8.4.General Characteristics of Various Methods for Linear Problems -- 8.5.Non-linear Hyperbolic Problems -- 8.6.Error Dynamics: Beyond von Neumann Analysis -- 8.6.1.Dispersion error and its quantification -- 8.7.Role of Group Velocity and Focussing -- 8.7.1.Focussing phenomenon -- ch. 9 Curvilinear Coordinate and Grid Generation -- 9.1.Introduction -- 9.2.Generalized Curvilinear Scheme -- 9.3.Reciprocal or Dual Base Vectors -- 9.4.Geometric Interpretation of Metrics -- 9.5.Orthogonal Grid System -- 9.6.Generalized Coordinate Transformation -- 9.7.Equations for the Metrics -- 9.8.Navier-Stokes Equation in the Transformed Plane -- 9.9.Linearization of Fluxes -- 9.10.Thin Layer Navier-Stokes Equation -- 9.11.Grid Generation -- 9.12.Types of Grid -- 9.13.Grid Generation Methods -- 9.14.Algebraic Grid Generation Method -- 9.14.1.One-dimensional stretching functions -- 9.15.Grid Generation by Solving Partial Differential Equations -- 9.16.Elliptic Grid Generators -- 9.17.Hyperbolic Grid Generation Method -- 9.18.Orthogonal Grid Generation for Navier-Stokes Computations -- 9.19.Coordinate Transformations and Governing Equations in Orthogonal System -- 9.19.1.Gradient operator -- 9.19.2.Divergence operator -- 9.19.3.The Laplacian operator -- 9.19.4.The curl operator -- 9.19.5.The line integral -- 9.19.6.The surface integral -- 9.19.7.The volume integral -- 9.20.The Gradient and Laplacian of Scalar Function -- 9.21.Vector Operators of a Vector Function -- 9.22.Plane Polar Coordinates -- 9.23.Navier-Stokes Equation in Orthogonal Formulation -- 9.24.Improved Orthogonal Grid Generation Method for Cambered Airfoils -- 9.24.1.Orthogonal grid generation for GA(W)-1 airfoil -- 9.24.2.Orthogonal grid generation for an airfoil with roughness element -- 9.24.3.Solutions of Navier-Stokes equation for flow past SHM-1 airfoil -- 9.24.4.Compressible flow past NACA 0012 airfoil -- 9.25.Governing Euler Equation, Auxiliary Conditions, Numerical Methods and Results -- 9.26.Flow Field Calculation Using Overset or Chimera Grid Technique -- ch.
10 Spectral Analysis of Numerical Schemes and Aliasing Error -- 10.1.Introduction -- 10.2.Spatial Discretization of First Derivatives -- 10.2.1.Second order central differencing (CD2) scheme -- 10.3.Discrete Computing and Nyquist Criterion -- 10.4.Spectral Accuracy of Differentiation -- 10.5.Spectral Analysis of Fourth Order Central Difference Scheme -- 10.6.Role of Upwinding -- 10.6.1.First order upwind scheme (UD1) -- 10.6.2.Third order upwind scheme (UD3) -- 10.7.Numerical Stability and Concept of Feedback -- 10.8.Spectral Stability Analysis -- 10.9.High Accuracy Schemes for Spatial Derivatives -- 10.10.Temporal Discretization Schemes -- 10.10.1.Euler time integration scheme -- 10.10.2.Four-stage Runge-Kutta (RK4) method -- 10.11.Multi-Time Level Discretization Schemes -- 10.11.1.Mid-point leapfrog scheme -- 10.11.2.Second order Adams-Bashforth scheme -- 10.12.Aliasing Error -- 10.12.1.Why aliasing error is important? -- 10.12.2.Estimation of aliased component -- 10.13.Numerical Estimates of Aliasing Error -- 10.14.Controlling Aliasing Error -- 10.14.1.Aliasing removal by zero padding -- 10.14.2.Aliasing removal by phase shifts and grid-staggering -- ch. 11 Higher Accuracy Methods -- 11.1.Introduction -- 11.2.The General Compact Schemes -- 11.2.1.Approximating first derivatives by central scheme -- 11.3.Method for Solving Periodic Tridiagonal Matrix Equation -- 11.4.An Example of a Sixth Order Scheme -- 11.5.Order of Approximation versus Resolution -- 11.6.Optimization Problem Associated with Discrete Evaluation of First Derivatives -- 11.7.An Optimized Compact Scheme For First Derivative by Grid Search Method -- 11.8.Upwind Compact Schemes -- 11.9.Compact Schemes with Improved Numerical Properties -- 11.9.1.OUCS1 scheme -- 11.9.2.OUCS2 scheme -- 11.9.3.OUCS3 scheme -- 11.9.4.OUCS4 scheme -- 11.10.Approximating Second Derivatives -- 11.11.Optimization Problem for Evaluation of the Second Derivatives -- 11.12.Solution of One-Dimensional Convection Equation -- 11.13.Symmetrized Compact Difference Schemes -- 11.13.1.High accuracy symmetrized compact scheme -- 11.13.2.Solving bidirectional wave equation -- 11.13.3.Transitional channel flow -- 11.13.3.1.Establishment of equilibrium flow -- 11.13.3.2.Receptivity of channel flow to convecting single viscous vortex -- 11.13.4.Transitional channel flow created by vortex street -- 11.14.Combined Compact Difference (CCD) Schemes -- 11.14.1.A new combined compact difference (NCCD) scheme -- 11.14.2.Solving the Stommel Ocean Model problem -- 11.14.3.Operational aspects of the CCD schemes -- 11.14.4.Calibrating NCCD method to solve Navier-Stokes equation for 2D lid-driven cavity problem -- 11.15.Diffusion Discretization and Dealiasing Properties of Compact Schemes -- 11.15.1.Dynamics and aliasing in square LDC problem --
Record Nr. UNINA-9910787623703321
Sengupta Tapan Kumar <1955->  
Cambridge : , : Cambridge University Press, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta
High accuracy computing methods : fluid flows and wave phenomena / / Tapan K. Sengupta
Autore Sengupta Tapan Kumar <1955->
Edizione [1st ed.]
Pubbl/distr/stampa Cambridge : , : Cambridge University Press, , 2013
Descrizione fisica 1 online resource (xix, 569 pages) : digital, PDF file(s)
Disciplina 532/.050285
Soggetto topico Fluid dynamics - Data processing
Wave mechanics - Data processing
Spectrum analysis - Data processing
ISBN 1-107-06965-3
1-107-05783-3
1-107-05456-7
1-107-05907-0
1-107-05561-X
1-139-15182-7
Classificazione COM000000
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Machine generated contents note: ch. 1 Basic Ideas of Scientific Computing -- 1.1.Overview on Scientific Computing -- 1.2.Major Milestones in Electronic Computing -- 1.3.Supercomputing and High Performance Computing -- 1.3.1.Parallel and cluster computing -- 1.3.2.Algorithmic issues of HPC -- 1.4.Computational Fluid Mechanics -- 1.5.Role of Computational Fluid Mechanics -- ch. 2 Governing Equations in Fluid Mechanics -- 2.1.Introduction -- 2.2.Basic Equations of Fluid Mechanics -- 2.2.1.Finite control volume -- 2.2.2.Infinitesimal fluid element -- 2.2.3.Substantive derivative -- 2.3.Equation of Continuity -- 2.4.Momentum Conservation Equation -- 2.5.Energy Conservation Equation -- 2.6.Alternate Forms of Energy Equation -- 2.7.The Energy Equation in Conservation Form -- 2.8.Notes on Governing Equations -- 2.9.Strong Conservation and Weak Conservation Forms -- 2.10.Boundary and Initial Conditions (Auxiliary Conditions) -- 2.11.Equations of Motion in Non-Inertial Frame -- 2.12.Equations of Motion in Terms of Derived Variables -- 2.13.Vorticity-Vector Potential Formulation -- 2.14.Pressure Poisson Equation -- 2.15.Comparison of Different Formulations -- 2.16.Other Forms of Navier-Stokes Equation -- ch. 3 Classification of Quasi-Linear Partial Differential Equations -- 3.1.Introduction -- 3.2.Classification of Partial Differential Equations -- 3.3.Relationship of Numerical Solution Procedure and Equation Type -- 3.4.Nature of Well-Posed Problems -- 3.5.Non-Dimensional Form of Equations -- ch. 4 Waves and Space-Time Dependence in Computing -- 4.1.Introduction -- 4.2.The Wave Equation -- 4.2.1.Plane waves -- 4.2.2.Three-dimensional axisymmetric wave -- 4.2.3.Doppler shift -- 4.2.4.Surface gravity waves -- 4.3.Deep and Shallow Water Waves -- 4.4.Group Velocity and Energy Flux -- 4.4.1.Physical and computational implications of group velocity -- 4.4.2.Wave-packets and their propagation -- 4.4.3.Waves over layer of constant depth -- 4.4.4.Waves over layer of variable depth H(x) -- 4.4.5.Wave refraction in shallow waters -- 4.4.6.Finite amplitude waves of unchanging form in dispersive medium -- 4.5.Internal Waves at Fluid Interface: Rayleigh-Taylor Problem -- 4.5.1.Internal and surface waves in finite over an infinite deep layer of fluid -- 4.5.2.Barotropic or surface mode -- 4.5.3.Baroclinic or internal mode -- 4.5.4.Rotating shallow water equation and wave dynamics -- 4.6.Shallow Water Equation (SWE) -- 4.6.1.Various frequency regimes of SWE -- 4.7.Additional Issues of Computing: Space-Time Resolution of Flows -- 4.7.1.Spatial scales in turbulent flows -- 4.8.Two- and Three-Dimensional DNS -- 4.9.Temporal Scales in Turbulent Flows -- 4.10.Computing Time-Averaged and Unsteady Flows -- ch. 5 Spatial and Temporal Discretizations of Partial Differential Equations -- 5.1.Introduction -- 5.2.Discretization of Differential Operators -- 5.2.1.Functional representation by the Taylor series -- 5.2.2.Polynomial representation of function -- 5.3.Discretization in Non-Uniform Grids -- 5.4.Higher Order Representation of Derivatives Using Operators -- 5.5.Higher Order Upwind Differences -- 5.5.1.Symmetric stencil for higher derivatives -- 5.6.Numerical Errors -- 5.7.Time Integration -- 5.7.1.Single-step methods -- 5.7.2.Single-step multi-stage methods -- 5.7.3.Runge-Kutta methods -- 5.7.4.Multi-step time integration schemes -- ch. 6 Solution Methods for Parabolic Partial Differential Equations -- 6.1.Introduction -- 6.2.Theoretical Analysis of the Heat Equation -- 6.3.A Classical Algorithm for Solution of the Heat Equation -- 6.4.Spectral Analysis of Numerical Methods -- 6.4.1.A higher order method or Milne's method -- 6.5.Treating Derivative Boundary Condition -- 6.6.Stability, Accuracy and Consistency of Numerical Methods -- 6.6.1.Richardson's method -- 6.6.2.Du Fort -- Frankel method -- 6.7.Implicit Methods -- 6.8.Spectral Stability Analysis of Implicit Methods -- Appendix I -- ch. 7 Solution Methods for Elliptic Partial Differential Equations -- 7.1.Introduction -- 7.2.Jacobi or Richardson Iteration -- 7.3.Interpretation of Classical Iterations -- 7.4.Different Point and Line Iterative Methods -- 7.4.1.Gauss-Seidel point iterative method -- 7.4.2.Line Jacobi method -- 7.4.3.Explanation of line iteration methods -- 7.5.Analysis of Iterative Methods -- 7.6.Convergence Theorem for Stationary Linear Iteration -- 7.7.Relaxation Methods -- 7.8.Efficiency of Iterative Methods and Rate of Convergence -- 7.8.1.Method of acceleration due to Lyusternik -- 7.9.Alternate Direction Implicit (ADI) Method -- 7.9.1.Analysis of ADI method -- 7.9.2.Choice of acceleration parameters -- 7.9.3.Estimates of maximum and minimum eigenvalues -- 7.9.4.Explanatory notes on ADI and other variant methods -- 7.10.Method of Fractional Steps -- 7.11.Multi-Grid Methods -- 7.11.1.Two-Grid method -- 7.11.2.Multi-Grid method -- 7.11.3.Other classifications of multi-grid method -- ch. 8 Solution of Hyperbolic PDEs: Signal and Error Propagation -- 8.1.Introduction -- 8.2.Classical Methods of Solving Hyperbolic Equations -- 8.2.1.Explicit methods -- 8.3.Implicit Methods -- 8.4.General Characteristics of Various Methods for Linear Problems -- 8.5.Non-linear Hyperbolic Problems -- 8.6.Error Dynamics: Beyond von Neumann Analysis -- 8.6.1.Dispersion error and its quantification -- 8.7.Role of Group Velocity and Focussing -- 8.7.1.Focussing phenomenon -- ch. 9 Curvilinear Coordinate and Grid Generation -- 9.1.Introduction -- 9.2.Generalized Curvilinear Scheme -- 9.3.Reciprocal or Dual Base Vectors -- 9.4.Geometric Interpretation of Metrics -- 9.5.Orthogonal Grid System -- 9.6.Generalized Coordinate Transformation -- 9.7.Equations for the Metrics -- 9.8.Navier-Stokes Equation in the Transformed Plane -- 9.9.Linearization of Fluxes -- 9.10.Thin Layer Navier-Stokes Equation -- 9.11.Grid Generation -- 9.12.Types of Grid -- 9.13.Grid Generation Methods -- 9.14.Algebraic Grid Generation Method -- 9.14.1.One-dimensional stretching functions -- 9.15.Grid Generation by Solving Partial Differential Equations -- 9.16.Elliptic Grid Generators -- 9.17.Hyperbolic Grid Generation Method -- 9.18.Orthogonal Grid Generation for Navier-Stokes Computations -- 9.19.Coordinate Transformations and Governing Equations in Orthogonal System -- 9.19.1.Gradient operator -- 9.19.2.Divergence operator -- 9.19.3.The Laplacian operator -- 9.19.4.The curl operator -- 9.19.5.The line integral -- 9.19.6.The surface integral -- 9.19.7.The volume integral -- 9.20.The Gradient and Laplacian of Scalar Function -- 9.21.Vector Operators of a Vector Function -- 9.22.Plane Polar Coordinates -- 9.23.Navier-Stokes Equation in Orthogonal Formulation -- 9.24.Improved Orthogonal Grid Generation Method for Cambered Airfoils -- 9.24.1.Orthogonal grid generation for GA(W)-1 airfoil -- 9.24.2.Orthogonal grid generation for an airfoil with roughness element -- 9.24.3.Solutions of Navier-Stokes equation for flow past SHM-1 airfoil -- 9.24.4.Compressible flow past NACA 0012 airfoil -- 9.25.Governing Euler Equation, Auxiliary Conditions, Numerical Methods and Results -- 9.26.Flow Field Calculation Using Overset or Chimera Grid Technique -- ch.
10 Spectral Analysis of Numerical Schemes and Aliasing Error -- 10.1.Introduction -- 10.2.Spatial Discretization of First Derivatives -- 10.2.1.Second order central differencing (CD2) scheme -- 10.3.Discrete Computing and Nyquist Criterion -- 10.4.Spectral Accuracy of Differentiation -- 10.5.Spectral Analysis of Fourth Order Central Difference Scheme -- 10.6.Role of Upwinding -- 10.6.1.First order upwind scheme (UD1) -- 10.6.2.Third order upwind scheme (UD3) -- 10.7.Numerical Stability and Concept of Feedback -- 10.8.Spectral Stability Analysis -- 10.9.High Accuracy Schemes for Spatial Derivatives -- 10.10.Temporal Discretization Schemes -- 10.10.1.Euler time integration scheme -- 10.10.2.Four-stage Runge-Kutta (RK4) method -- 10.11.Multi-Time Level Discretization Schemes -- 10.11.1.Mid-point leapfrog scheme -- 10.11.2.Second order Adams-Bashforth scheme -- 10.12.Aliasing Error -- 10.12.1.Why aliasing error is important? -- 10.12.2.Estimation of aliased component -- 10.13.Numerical Estimates of Aliasing Error -- 10.14.Controlling Aliasing Error -- 10.14.1.Aliasing removal by zero padding -- 10.14.2.Aliasing removal by phase shifts and grid-staggering -- ch. 11 Higher Accuracy Methods -- 11.1.Introduction -- 11.2.The General Compact Schemes -- 11.2.1.Approximating first derivatives by central scheme -- 11.3.Method for Solving Periodic Tridiagonal Matrix Equation -- 11.4.An Example of a Sixth Order Scheme -- 11.5.Order of Approximation versus Resolution -- 11.6.Optimization Problem Associated with Discrete Evaluation of First Derivatives -- 11.7.An Optimized Compact Scheme For First Derivative by Grid Search Method -- 11.8.Upwind Compact Schemes -- 11.9.Compact Schemes with Improved Numerical Properties -- 11.9.1.OUCS1 scheme -- 11.9.2.OUCS2 scheme -- 11.9.3.OUCS3 scheme -- 11.9.4.OUCS4 scheme -- 11.10.Approximating Second Derivatives -- 11.11.Optimization Problem for Evaluation of the Second Derivatives -- 11.12.Solution of One-Dimensional Convection Equation -- 11.13.Symmetrized Compact Difference Schemes -- 11.13.1.High accuracy symmetrized compact scheme -- 11.13.2.Solving bidirectional wave equation -- 11.13.3.Transitional channel flow -- 11.13.3.1.Establishment of equilibrium flow -- 11.13.3.2.Receptivity of channel flow to convecting single viscous vortex -- 11.13.4.Transitional channel flow created by vortex street -- 11.14.Combined Compact Difference (CCD) Schemes -- 11.14.1.A new combined compact difference (NCCD) scheme -- 11.14.2.Solving the Stommel Ocean Model problem -- 11.14.3.Operational aspects of the CCD schemes -- 11.14.4.Calibrating NCCD method to solve Navier-Stokes equation for 2D lid-driven cavity problem -- 11.15.Diffusion Discretization and Dealiasing Properties of Compact Schemes -- 11.15.1.Dynamics and aliasing in square LDC problem --
Record Nr. UNINA-9910818842103321
Sengupta Tapan Kumar <1955->  
Cambridge : , : Cambridge University Press, , 2013
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