## 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

## Dynamics of Viscous Compressible Fluids

*Eduard Feireisl*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528388
- eISBN:
- 9780191713590
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528388.001.0001
- Subject:
- Mathematics, Applied Mathematics

The book presents and develops the most recent ideas and concepts of the mathematical theory of viscous, compressible, and heat conducting fluids. Two main objectives are pursued: (i) global ... 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

## 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

## 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

## 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

## 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

## 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

## VARIATIONAL SOLUTIONS

*Eduard Feireisl*

### in Dynamics of Viscous Compressible Fluids

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528388
- eISBN:
- 9780191713590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528388.003.0004
- Subject:
- Mathematics, Applied Mathematics

The concept of a variational solution to the full Navier-Stokes-Fourier system is introduced in this chapter. Each equation of the complete system, that means, the equation of continuity, the ... More

## GLOBAL EXISTENCE

*Eduard Feireisl*

### in Dynamics of Viscous Compressible Fluids

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528388
- eISBN:
- 9780191713590
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528388.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter contains a complete proof of the existence of global-in-time variational solutions for the full system of the Navier-Stokes equations of a viscous compressible and heat conducting fluid ... 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## 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

## Introduction to Engineering Fluid Mechanics

*Marcel Escudier*

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198719878
- eISBN:
- 9780191840180
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198719878.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Turbojet and turbofan engines, rocket motors, road vehicles, aircraft, pumps, compressors, and turbines are examples of machines which require a knowledge of fluid mechanics for their design. The aim ... More