## 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

## Electromechanics and its devices

*Sandip Tiwari*

### in Nanoscale Device Physics: Science and Engineering Fundamentals

- Published in print:
- 2017
- Published Online:
- August 2017
- ISBN:
- 9780198759874
- eISBN:
- 9780191820847
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198759874.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

Electromechanics—coupling of mechanical forces with others—exhibits a continuum-to-discrete spectrum of properties. In this chapter, classical and newer analysis techniques are developed for devices ... 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