Numerical methods in turbulence simulation

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...

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Detalles Bibliográficos
Otros Autores:	Moser, Robert deLancey, editor (editor)
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	London, England ; San Diego, California : Academic Press [2023]
Colección:	Numerical Methods in Turbulence
Materias:	Turbulence > Mathematics. Turbulence > Simulation methods.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009835431306719

Tabla de Contenidos:

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.
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.
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.
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.
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.
11.3.3 Example: impact of energy preservation.

Numerical methods in turbulence simulation

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