George Karniadakis and Spencer Sherwin
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.001.0001
- Subject:
- Mathematics, Numerical Analysis
Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more ...
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Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application.Less
Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application.
Raymond Brun
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199552689
- eISBN:
- 9780191720277
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199552689.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter presents the general features of traditional gas dynamics, deduced from the ideal gas model assuming no reaction and constant specific heats. Examples are given including one-dimensional ...
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This chapter presents the general features of traditional gas dynamics, deduced from the ideal gas model assuming no reaction and constant specific heats. Examples are given including one-dimensional isentropic flows, shock waves, and boundary layers. In the framework of these examples, various flow configurations are considered such as expanding flows in nozzles, kinematics of shock waves, and boundary layers with and without pressure gradient, and turbulent flows. Calculation methods of flow quantities are presented, such as the method of characteristics for isentropic flows, Rankine-Hugoniot relations for shock waves, and Lees-Levy-Dorodnitsin (LLD) transformation for boundary layers.Less
This chapter presents the general features of traditional gas dynamics, deduced from the ideal gas model assuming no reaction and constant specific heats. Examples are given including one-dimensional isentropic flows, shock waves, and boundary layers. In the framework of these examples, various flow configurations are considered such as expanding flows in nozzles, kinematics of shock waves, and boundary layers with and without pressure gradient, and turbulent flows. Calculation methods of flow quantities are presented, such as the method of characteristics for isentropic flows, Rankine-Hugoniot relations for shock waves, and Lees-Levy-Dorodnitsin (LLD) transformation for boundary layers.
Damien Violeau
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655526
- eISBN:
- 9780191741227
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655526.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book aims at presenting the SPH method for fluid modelling from a theoretical and applied viewpoint. It comprises two parts that refer to each other. The first, dealing with the fundamentals of ...
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This book aims at presenting the SPH method for fluid modelling from a theoretical and applied viewpoint. It comprises two parts that refer to each other. The first, dealing with the fundamentals of Hydraulics, is based on the elementary principles of Lagrangian and Hamiltonian mechanics. The specific laws governing a system of macroscopic particles are built, then the large systems involving dissipative processes are explained. The continua are then discussed; lastly, a fairly exhaustive account of turbulence is given. The second part discloses the bases of the SPH Lagrangian numerical method from the continuous equations, as well as from discrete variational principles, setting out the method's specific properties of conservativity and invariance. Various numerical schemes are compared, permanently referring to physics as dealt with in the first part. Applications to schematic instances are then discussed; ultimately, practical applications to the dimensioning of coastal and fluvial structures are considered. Despite the rapid growth in the SPH field, this book is the first to present this method in a comprehensive way for fluids. It should serve as a rigorous introduction to SPH and a reference for fundamental mathematical fluid dynamics.Less
This book aims at presenting the SPH method for fluid modelling from a theoretical and applied viewpoint. It comprises two parts that refer to each other. The first, dealing with the fundamentals of Hydraulics, is based on the elementary principles of Lagrangian and Hamiltonian mechanics. The specific laws governing a system of macroscopic particles are built, then the large systems involving dissipative processes are explained. The continua are then discussed; lastly, a fairly exhaustive account of turbulence is given. The second part discloses the bases of the SPH Lagrangian numerical method from the continuous equations, as well as from discrete variational principles, setting out the method's specific properties of conservativity and invariance. Various numerical schemes are compared, permanently referring to physics as dealt with in the first part. Applications to schematic instances are then discussed; ultimately, practical applications to the dimensioning of coastal and fluvial structures are considered. Despite the rapid growth in the SPH field, this book is the first to present this method in a comprehensive way for fluids. It should serve as a rigorous introduction to SPH and a reference for fundamental mathematical fluid dynamics.
Peter Davidson
- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198722588
- eISBN:
- 9780191789298
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722588.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics
This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the ...
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This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth.Less
This book presents the subject of turbulence. The aim of the book is to bridge the gap between the elementary, heuristic accounts of turbulence and the more rigorous accounts given. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth.
Jill Lancaster and Barbara J. Downes
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199573219
- eISBN:
- 9780191774850
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573219.003.0005
- Subject:
- Biology, Aquatic Biology, Animal Biology
This chapter first discusses some of the physical properties of water, including viscosity, water pressure, and the surface films formed between water and air. With these principles in mind, it then ...
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This chapter first discusses some of the physical properties of water, including viscosity, water pressure, and the surface films formed between water and air. With these principles in mind, it then explains how living in water affects the morphology and behaviour of aquatic insects that live in different habitats. In still water, buoyancy and the problem of maintaining position in the water column or on the substrate are perhaps the major challenges. Insects that live on the water surface must avoid sinking and they use various strategies that exploit the physical properties of surface films and hydrofuge or water-repellent body parts. The section on life in flowing waters begins with a discussion of some physical properties including Reynolds numbers, drag, shear stress, streamlining, laminar and turbulent flows, and boundary layers. These physical properties shape the various adaptations to flowing water, most of which centre on the need to reduce drag when moving and feeding, and to avoid accidental displacement.Less
This chapter first discusses some of the physical properties of water, including viscosity, water pressure, and the surface films formed between water and air. With these principles in mind, it then explains how living in water affects the morphology and behaviour of aquatic insects that live in different habitats. In still water, buoyancy and the problem of maintaining position in the water column or on the substrate are perhaps the major challenges. Insects that live on the water surface must avoid sinking and they use various strategies that exploit the physical properties of surface films and hydrofuge or water-repellent body parts. The section on life in flowing waters begins with a discussion of some physical properties including Reynolds numbers, drag, shear stress, streamlining, laminar and turbulent flows, and boundary layers. These physical properties shape the various adaptations to flowing water, most of which centre on the need to reduce drag when moving and feeding, and to avoid accidental displacement.
Anthony Leonard
- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195106435
- eISBN:
- 9780197561003
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195106435.003.0006
- Subject:
- Computer Science, Mathematical Theory of Computation
The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem ...
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The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem by numerical simulation. But one could point to a beginning 20 years later when Deardorff (1970) reported on a large-eddy simulation of turbulent channel flow on a 24x20x14 mesh and a direct simulation of homogeneous, isotropic turbulence was accomplished on a 323 mesh by Orszag and Patterson (1972). Perhaps the arrival of the CDC 6600 triggered these initial efforts. Since that time, a number of developments have occurred along several fronts. Of course, faster computers with more memory continue to become available and now, in 1994, 2563 simulations of homogeneous turbulence are relatively common with occasional 5123 simulations being achieved on parallel supercomputers (Chen et al., 1993) (Jimenez et al., 1993). In addition, new algorithms have been developed which extend or improve capabilities in turbulence simulation. For example, spectral methods for the simulation of arbitrary homogeneous flows and the efficient simulation of wall-bounded flows have been available for some time for incompressible flows and have recently been extended to compressible flows. In addition fast, viscous vortex methods and spectral element methods are now becoming available, suitable for incompressible flow with complex geometries. As a result of all these developments, the number of turbulence simulations has been increasing rapidly in the past few years and will continue to do so. While limitations exist (Reynolds, 1990; Hussaini et al., 1990), the potential of the method will lead to the simulation of a wide variety of turbulent flows. In this chapter, we present examples of these new developments and discuss prospects for future developments.
Less
The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem by numerical simulation. But one could point to a beginning 20 years later when Deardorff (1970) reported on a large-eddy simulation of turbulent channel flow on a 24x20x14 mesh and a direct simulation of homogeneous, isotropic turbulence was accomplished on a 323 mesh by Orszag and Patterson (1972). Perhaps the arrival of the CDC 6600 triggered these initial efforts. Since that time, a number of developments have occurred along several fronts. Of course, faster computers with more memory continue to become available and now, in 1994, 2563 simulations of homogeneous turbulence are relatively common with occasional 5123 simulations being achieved on parallel supercomputers (Chen et al., 1993) (Jimenez et al., 1993). In addition, new algorithms have been developed which extend or improve capabilities in turbulence simulation. For example, spectral methods for the simulation of arbitrary homogeneous flows and the efficient simulation of wall-bounded flows have been available for some time for incompressible flows and have recently been extended to compressible flows. In addition fast, viscous vortex methods and spectral element methods are now becoming available, suitable for incompressible flow with complex geometries. As a result of all these developments, the number of turbulence simulations has been increasing rapidly in the past few years and will continue to do so. While limitations exist (Reynolds, 1990; Hussaini et al., 1990), the potential of the method will lead to the simulation of a wide variety of turbulent flows. In this chapter, we present examples of these new developments and discuss prospects for future developments.
