## 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