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ALGORITHMS FOR INCOMPRESSIBLE FLOWS

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0008
Subject:
Mathematics, Numerical Analysis

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. ... More


HYPERBOLIC CONSERVATION LAWS

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0010
Subject:
Mathematics, Numerical Analysis

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the ... More


INCOMPRESSIBLE FLOW SIMULATIONS: VERIFICATION AND VALIDATION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0009
Subject:
Mathematics, Numerical Analysis

This chapter discusses numerical simulations of the incompressible Navier-Stokes equations. Exact Navier-Stokes solutions are presented that are used as benchmarks to validate new codes and evaluate ... More


INTRODUCTION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0001
Subject:
Mathematics, Numerical Analysis

This chapter presents reduced models of the compressible and incompressible Navier-Stokes equations which are used in the various discretization concepts discussed in the rest of the book. The ... More


MATHEMATICAL ANALYSIS OF ONE-FLUID PROBLEMS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0002
Subject:
Mathematics, Mathematical Physics

This chapter focuses on the modelling of one-fluid magnetohydrodynamics problems. The crucial point under consideration is the coupling between hydrodynamics phenomena and electromagnetic phenomena. ... More


THE MAGNETOHYDRODYNAMICS EQUATIONS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0001
Subject:
Mathematics, Mathematical Physics

This chapter presents how MHD equations can be derived from the general conservation equations for fluid mechanics coupled with the Maxwell equations modelling the electromagnetic phenomena. A ... More


Continuous media and viscous fluids

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655526
eISBN:
9780191741227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655526.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

Continuous media are here seen from the traditional viewpoint of balance equations; the chapter introduces the concepts of mesoscopic particles, fields and fluxes. The conservation laws of the first ... More


Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.001.0001
Subject:
Mathematics, Mathematical Physics

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and ... More


Partial differential equations for fluids

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199546909
eISBN:
9780191720482
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546909.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ... More


Boundary-Layer Separation

Anatoly I. Ruban

in Fluid Dynamics: Part 3 Boundary Layers

Published in print:
2017
Published Online:
January 2018
ISBN:
9780199681754
eISBN:
9780191761621
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199681754.003.0003
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Chapter 2 discusses the experimental observations of the boundary-layer separation in subsonic and supersonic flows that lead to a formulation of the concept of viscous-inviscid interaction. It then ... More


General Aspects of Gas Flows

Raymond Brun

in Introduction to Reactive Gas Dynamics

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199552689
eISBN:
9780191720277
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552689.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the Navier-Stokes equations for a gaseous system in vibrational and/or chemical non-equilibrium, and proposes various forms. The equations are written in a dimensionless form so ... More


Transport and Relaxation in Quasi-Equilibrium Regimes: Pure Gases

Raymond Brun

in Introduction to Reactive Gas Dynamics

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199552689
eISBN:
9780191720277
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552689.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter expands the distribution function of a pure gas in a series of a small parameter representing the ratio of the collisional time to a reference flow time; this is the so-called ... More


Fundamentals of Fluid Dynamics

Anatoly I. Ruban and Jitesh S. B. Gajjar

in Fluid Dynamics: Part 1: Classical Fluid Dynamics

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199681730
eISBN:
9780191761607
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681730.003.0002
Subject:
Physics, Soft Matter / Biological Physics

This chapter starts with a discussion of the continuum hypothesis and the conditions under which it can be used. The origin of the internal forces acting in moving fluids is then identified and the ... More


Discontinuous Galerkin methods (DCGMs), with V. Dolejší

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 7 presents with V. Dolejší presents discontinuous Galerkin methods (DCGMs): violated boundary conditions and continuity of the piecewise polynomials are compensated by additional penalty ... More


ION TRANSPORT IN NORMAL LIQUID 4HE

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0016
Subject:
Physics, Condensed Matter Physics / Materials

Ions are used in normal liquid helium to investigate the hydrodynamics in presence of electrostriction. The Navier-Stokes equation must be modified in order to account for the spatial variations of ... More


From linear to nonlinear equations, fundamental results

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 1 demonstrates, for the simple mechanical example of a bent rod, the change in character from linear to nonlinear regimes. This is followed by several examples for different types of ... More


Stokes’s Fundamental Contributions to Fluid Dynamics

Peter Lynch

in George Gabriel Stokes: Life, Science and Faith

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198822868
eISBN:
9780191861321
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822868.003.0006
Subject:
Mathematics, History of Mathematics

George Gabriel Stokes made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him play a central role in numerical ... More


The Scientific Legacy of George Gabriel Stokes

Andrew Fowler

in George Gabriel Stokes: Life, Science and Faith

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198822868
eISBN:
9780191861321
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822868.003.0011
Subject:
Mathematics, History of Mathematics

The scientific legacy of George Gabriel Stokes is considered. Certain aspects of Stokes’s research work are reviewed and related to more recent fields of research. These include the Navier–Stokes ... More


ION TRANSPORT AT PHASE TRANSITIONS

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0017
Subject:
Physics, Condensed Matter Physics / Materials

At T=2.17 K and P=0, liquid helium undergoes the superfluid transition. Dose this transition belong to the same universality class of the usual liquid-vapor transition? This question has been ... More


Fluid Dynamics: Part 1: Classical Fluid Dynamics

Anatoly I. Ruban and Jitesh S. B. Gajjar

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199681730
eISBN:
9780191761607
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681730.001.0001
Subject:
Physics, Soft Matter / Biological Physics

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum ... More


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