| Description |
1 online resource. |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Computation and analysis of turbulent flows
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| Bibliography |
Includes bibliographical references and index. |
| Note |
Description based on online resource; title from digital title page (viewed on March 07, 2023). |
| Summary |
Numerical Methods in Turbulence Simulation provides detailed specifications of the numerical methods needed to solve important problems in turbulence simulation. Numerical simulation of turbulent fluid flows is challenging because of the range of space and time scales that must be represented. This book provides explanations of the numerical error and stability characteristics of numerical techniques, along with treatments of the additional numerical challenges that arise in large eddy simulations. Chapters are written as tutorials by experts in the field, covering specific both contexts and applications. Three classes of turbulent flow are addressed, including incompressible, compressible and reactive, with a wide range of the best numerical practices covered. A thorough introduction to the numerical methods is provided for those without a background in turbulence, as is everything needed for a thorough understanding of the fundamental equations. The small scales that must be resolved are generally not localized around some distinct small-scale feature, but instead are distributed throughout a volume. These characteristics put particular strain on the numerical methods used to simulate turbulent flows. Includes a detailed review of the numerical approximation issues that impact the simulation of turbulence Provides a range of examples of large eddy simulation techniques Discusses the challenges posed by boundary conditions in turbulence simulation and provides approaches to addressing them. |
| Contents |
Front Cover -- Numerical Methods in Turbulence Simulation -- Copyright -- Contents -- Contributors -- Preface -- 1 Numerical challenges in turbulence simulation -- 1.1 A brief introduction to turbulence -- 1.1.1 The nature of turbulence -- 1.1.2 The Navier-Stokes equations -- 1.1.3 Turbulence scaling -- 1.2 Numerical discretization of convection -- 1.2.1 Spectra of discrete first derivative operators -- 1.2.2 Numerical dispersion -- 1.2.3 Numerical dissipation -- 1.2.4 Resolution versus order of accuracy -- 1.2.5 Nonuniform grids -- 1.2.6 Nonlinearity and aliasing -- 1.2.7 Energy conservation -- 1.3 Numerical discretization of diffusion -- 1.3.1 Spectra of discrete second derivative operators -- 1.3.2 Numerical representation of dissipation -- 1.3.3 Impact of variable diffusivity -- 1.4 Numerical time discretization -- 1.4.1 Time accuracy -- 1.4.2 Time step stability -- Acknowledgments -- References -- 2 Spectral numerical methods for turbulence simulation -- 2.1 Motivation -- 2.2 General characteristics of spectral methods -- 2.2.1 Expansion functions and approximation properties -- 2.2.2 A convection-diffusion model problem -- 2.2.2.1 Weighted residual methods -- 2.2.2.2 Collocation methods -- 2.2.3 Navier-Stokes -- 2.3 Fourier spectral methods -- 2.3.1 Properties of Fourier series -- 2.3.2 Discrete Fourier transform -- 2.3.3 Aliasing, Gauss quadrature, and Galerkin approximations -- 2.3.4 Resolution and domain size -- 2.4 Orthogonal polynomials -- 2.4.1 Orthogonal polynomial properties -- 2.4.2 Gauss quadrature -- 2.4.3 Chebyshev polynomials -- 2.5 Spectral methods with polynomial bases -- 2.5.1 Computing nonlinear terms -- 2.5.2 Finite domains with Legendre and Chebyshev polynomials -- 2.5.2.1 Matrix structure -- 2.5.2.2 Numerical characteristics -- 2.5.3 Spectral methods for infinite domains -- 2.6 Time discretization for spectral methods. |
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Acknowledgments -- References -- 3 Spectral element methods for turbulence -- 3.1 Introduction -- 3.2 Advection-diffusion in a single deformed element -- 3.3 The multielement case -- 3.4 PN-PN formulation for incompressible flows -- 3.5 PN-PN formulation for low-Mach-number flows -- 3.6 Computing the pressure -- 3.7 Practical aspects -- 3.7.1 Stabilization techniques -- 3.7.2 Outflow boundary conditions -- 3.8 Example applications -- References -- 4 Spline-based methods for turbulence -- 4.1 Introduction -- 4.2 A brief introduction to splines -- 4.2.1 Univariate B-splines -- 4.2.2 Multivariate B-splines -- 4.2.3 Mapping to physical domains -- 4.2.4 Extension to multipatch domains -- 4.2.5 Local refinement of multivariate B-splines -- 4.2.6 Representation in terms of classical finite element bases -- 4.3 Spline-based methods for incompressible flows -- 4.3.1 The strong form of the incompressible flow problem -- 4.3.2 The weak form of the incompressible flow problem -- 4.3.3 Spatial discretization using a spline collocation method -- 4.3.4 Spatial discretization using a spline Galerkin method -- 4.3.5 Temporal discretization -- 4.4 A selection of spline velocity/pressure pairs -- 4.5 Stabilized spline-based methods -- References -- 5 Finite element methods for turbulence -- 5.1 Introduction -- 5.2 Discretization foundations -- 5.2.1 Basis functions -- 5.2.2 Time integration -- 5.3 Finite element formulations -- 5.3.1 Scalar advection-diffusion -- 5.3.1.1 Weak form -- 5.3.1.2 Numerical examples -- Advection in one direction -- Advection in a rotating flow field -- 5.3.2 Compressible Navier-Stokes -- 5.3.3 Low-Mach and incompressible Navier-Stokes -- 5.3.3.1 Strong form -- 5.3.3.2 Weak form -- finite element discretization -- 5.3.3.3 Local reconstruction of diffusive flux -- 5.3.3.4 Discrete system of equations -- 5.3.3.5 Numerical examples. |
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Kovasznay flow -- 5.4 Implementation -- 5.4.1 Data structures and performance implications -- 5.4.2 Matrix and matrix-free implicit solvers -- 5.4.3 Unstructured grid filtering for LES -- 5.4.3.1 Face-based filtering -- 5.4.3.2 Derivative-based filter -- 5.4.3.3 Generalized top-hat filter -- 5.4.3.4 Function based filter -- 5.5 Scale resolving turbulence simulations -- References -- 6 Finite difference methods for turbulence simulations -- 6.1 Introduction -- 6.2 Grid topologies -- 6.2.1 Navier-Stokes equations in curvilinear coordinates -- 6.2.1.1 Conservation laws on curvilinear grids -- 6.2.1.2 The geometric conservation constraint -- 6.2.2 Cartesian octree topologies -- 6.2.3 Numerical considerations for abrupt grid changes -- 6.3 Grid staggering and flux evaluations -- 6.3.1 Primitive variable placement -- 6.3.2 Staggered flux evaluations in collocated variable formulation -- 6.4 Robustness of inviscid flux discretization -- 6.4.1 Linear schemes -- 6.4.1.1 Kinetic energy preservation and entropy consistency -- 6.4.2 Flows with discontinuities -- 6.4.2.1 Nonlinear schemes: WENO interpolation and WCNS -- 6.4.2.2 Artificial dissipation -- 6.5 Finite difference schemes for LES: dispersion/dissipation errors -- 6.5.1 Are low-dispersion error schemes relevant for LES in turbulence-dominated flows? -- 6.5.2 Are shock-capturing schemes suitable to be used for LES? -- 6.5.3 Blended schemes -- 6.6 Discretization challenges specific to incompressible flows -- 6.7 Additional considerations -- 6.7.1 Boundary treatments -- 6.7.2 Time integration -- 6.7.3 Additional topics -- 6.8 Summarizing remarks -- References -- 7 Unstructured finite volume approaches for turbulence -- 7.1 Introduction -- 7.2 Finite volume discretization -- 7.2.1 Basis definition -- 7.2.2 Time derivative and source terms -- 7.2.3 Advection -- 7.2.4 Diffusion. |
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7.3 High Peclet number advection and diffusion -- 7.3.1 Residual-based stabilization -- 7.4 Transient advection and diffusion illustration -- 7.5 Low-Mach solver strategies -- 7.6 Low-Mach fluids operators -- 7.6.1 Kinetic energy conservation -- 7.7 Validation -- Acknowledgments -- References -- 8 Boundary conditions for turbulence simulation -- 8.1 Introduction -- 8.2 A motivating example -- 8.2.1 Continuous case -- 8.2.2 Discretization -- 8.2.3 Lessons learned -- 8.3 General framework -- 8.3.1 Physical BCs -- 8.3.2 Artificial BCs -- 8.3.3 Symmetry BCs -- 8.4 BCs for compressible Navier-Stokes -- 8.4.1 The characteristic BC framework -- 8.4.2 Refinements and extensions -- 8.4.2.1 Viscous flow -- 8.4.2.2 Rigid-wall no-slip BC -- 8.4.2.3 Inlet/outlet impedance: taming drift -- 8.4.2.4 Sponge layers for multidimensional nonreflectivity -- 8.4.2.5 Other extensions -- 8.4.3 Summation-by-parts approach -- 8.4.4 Case study: high-speed turbulent jet -- 8.5 BCs for incompressible Navier-Stokes -- 8.5.1 Rigid no-slip and inlet BCs -- 8.5.2 Far-field BCs -- 8.5.3 Outlet BCs -- 8.5.4 Dealing with pressure -- 8.5.5 Case study: flow over a sphere -- 8.6 Turbulence modeling in boundary conditions -- 8.6.1 Triggering natural instabilities -- 8.6.2 Synthetic turbulence injection -- 8.7 BCs in other discretization schemes -- 8.7.1 Other schemes with body-fitted meshes -- 8.7.2 Non-conforming BCs: immersed boundary and interface methods -- References -- 9 Numerical methods in large-eddy simulation -- 9.1 Scope of the chapter -- 9.2 Large-eddy simulation: from practice to theory -- 9.2.1 LES: statement of the problem -- 9.2.2 Removal of small scales in LES: mathematical models for the LES filter -- 9.2.2.1 The filtered Navier-Stokes equations model -- 9.2.2.2 A more realistic model: the twice-filtered Navier-Stokes equations. |
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9.2.3 Explicitly filtered LES and the grid convergence issue -- 9.3 Implicit coupling between numerics and explicit subgrid models -- 9.3.1 Statement of the problem -- 9.3.2 A first analysis via Taylor expansions -- 9.3.3 Static and dynamic analysis -- 9.3.4 Observations in nonhomogeneous flows -- 9.3.4.1 Plane channel flow case -- 9.3.4.2 Circular cylinder case -- 9.4 LES numerics: beyond order of accuracy -- 9.4.1 Statement of the problem -- 9.4.2 Structure-preserving schemes for LES -- 9.4.3 Extension to LES of compressible flows -- 9.5 Concluding remarks -- References -- 10 Numerical approximations formulated as LES models -- 10.1 Coarse grained simulations -- 10.1.1 Introduction -- 10.1.2 Low-pass filtered and finite-volume discretized Navier-Stokes equations -- 10.1.3 Modified equation analysis of subgrid scale modeling -- 10.1.3.1 Finite scale Navier-Stokes -- 10.1.3.2 Spatial filtering and ensemble averaging -- 10.2 Turbulence Reynolds number and mixing transition -- 10.2.1 Effective kinematic viscosity -- 10.3 Compressible numerical hydrodynamics -- 10.3.1 Riemann solvers -- 10.3.2 Low-Ma correction -- 10.3.3 Modified equation analysis -- 10.4 Case studies -- 10.4.1 Taylor-Green vortex -- 10.4.1.1 Impact of numerical scheme on quantities of interest -- 10.4.1.2 Numerical Reynolds number -- 10.4.2 Accelerated interface Rayleigh-Taylor driven mixing -- 10.4.2.1 Impact of numerical scheme on quantities of interest -- 10.4.2.2 Numerical Reynolds number -- 10.5 Summary and conclusions -- Acknowledgments -- References -- 11 Numerical treatment of incompressible turbulent flow -- 11.1 Introduction -- 11.1.1 Numerical challenge -- 11.1.2 Short history of energy-preserving discretization -- 11.1.3 Turbulence modeling -- 11.2 Flow equations -- 11.3 Energy-preserving discretization -- 11.3.1 Finite-volume -- 11.3.2 Evolution of energy. |
| Subject |
Turbulence -- Mathematics.
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Turbulence -- Simulation methods.
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Turbulence -- Mathématiques.
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Turbulence -- Méthodes de simulation.
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Turbulence -- Mathematics
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Turbulence -- Simulation methods
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| Added Author |
Moser, Robert deLancey, editor.
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| Other Form: |
Print version: 9780323998338 |
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Print version: 0323911447 9780323911443 (OCoLC)1294289174 |
| ISBN |
9780323998338 electronic book |
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032399833X electronic book |
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9780323911443 |
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0323911447 |
| Standard No. |
UKMGB 020773240 |
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AU@ 000073296424 |
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