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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


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