Table Of ContentLecture Notes in Physics
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G. Bodo
S. Massaglia
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A. Mignone
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P. Rossi (Eds.)
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Jets From Young Stars III
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Numerical MHD and Instabilities
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Editors
GianluigiBodo SilvanoMassaglia
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OsservatorioAstronomicodi Universita` diTorino
Torino Dipto.FisicaGenerale
StradaOsservatorio,20 ViaPietroGiuria,1 O
10025PinoTorineseTO 10125Torino
Italy Italy
[email protected] [email protected] O
AndreaMignone PaolaRossi
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Universita` diTorino INAFOsservatorio
Dipto.FisicaGenerale diTorinoAstronomico
ViaPietroGiuria,1 VialeOsservatorio,20
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10125Torino 10025PinoTorinese
Italy Italy
[email protected] [email protected] .it
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Bodo,G.etal.(Eds.),JetsFromYoungStarsIII,Lect.NEotesPhys.754(Springer,Berlin
Heidelberg2008),DOI10.1007/978-3-540-76967-5
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ISBN:978-3-540-76966-8 e-ISBN:978-3-540-76967-5
DOI10.1007/978-3-540-76967-5 E
LectureNotesinPhysicsISSN:0075-8450 e-ISSN:1616-6361
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LibraryofCongressControlNumber:2008927516
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(cid:2)c 2008Springer-VerlagBerlinHeidelberg
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Preface F
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The study of the mechanisms that govern origin andPpropagation of stellar
jets involves the treatment of many concurrent physical processes such as
gravitation, hydrodynamics and magnetohydrodynamics, atomic physics and
radiation.Inthepastyears,anintensiveworkhasbeendonelookingforsolu-
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tions of the ideal MHD equations in thesteady state limit as well as studying
the stability of outflows in the linear regime. These kind, of approaches have
provided a contribution to the understandingEof jets that can hardly be over-
estimated. However, the extension of the analyses to the time-dependent and
nonlinear regimes could not be avoided, anTd the MHD numerical simulations
were the only mean to achieve this goal.
Intherecentyears,considerableproCgresseshavebeenmadebythecompu-
tationalfluiddynamiccommunityinthedevelopmentofnumericaltechniques,
theso-calledhighresolutionshockcapturingschemes,wellsuitedforthetreat-
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ment of supersonic flows with discontinuities. The numerical simulations of
astrophysicaljetstookadvantageofthesedevelopments;howevernewphysics
needed to be incorporated, suchRas magnetic field effects, radiation losses by
diluted gases, and proper astrophysics environments. These needs led to the
nontrivial extension of the methods devised for the Euler equations of gas-
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dynamics to the magneto-hydrodynamical system. On the other hand, the
possibility of carrying out numerical calculations has been greatly facilitated
bytheavailability,ononeOhand,ofpowerfulsupercomputersand,ontheother
hand,offastprocessorsatlowcost.Largescale3Dsimulationsofjetsathigh
resolution are now possible thanks to supercomputers, but also high resolu-
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tion 2D MHD simulations can be performed routinely on desktop computers.
These possibilities have greatly extended our understanding of jets, and nu-
merical simulations are now an essential tool for investigating the physics of
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such objects.
This book collects the lectures from the third JETSET school, Jets from
Young Stars UIII: Numerical MHD and Instabilities, held in Sauze d’Oulx in
January 2007. The aim of this school was to introduce PhD students and
young researchers to the basic methods in computational hydrodynamics and
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magneto-hydrodynamics as well as to review some of the most relevant insta-
bilities in astrophysical outflows.
The book is divided in two parts. In the first one, Eleuterio Toro presents
and discusses the basic numerical methods in hydrodynamics, their stabil-
ity, monotonicity and accuracy properties, and introduces different RFiemann
solvers and flux limiter methods. Andrea Mignone and Gianluigi Bodo then
extend the discussion to MHD, examining, in particular, the varioOus methods
devisedtoovercomethenumericaldifficultiesintrinsictotheMHDequations.
The second part is devoted to hydrodynamic and MHD instabilities, such as
theKelvin–Helmholtzinstabilities,treatedbyEdoardoTrussoOni,thepressure
driven instabilities, by Pierre-Yves Longaretti, the thermal instabilities, by
GianluigiBodo,andtheinstabilitiesinradiativeshocks,byAndreaMignone.
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The editors are grateful to the lecturers for their presentations and efforts
to contribute to this book, and to Ovidiu Tesileanu and Titos Matsakos that
havebeenofgreathelpintheorganizationoftheschooPl.ThanksalsotoEileen
Flood and Gabriella Ardizzoia for their precious help in managing the life of
the participants during the days of the school. The editors acknowledge the
invaluable contribution and support by Emma Whelan for taking care of the
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book editing.
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Torino Silvano Massaglia
Andrea Mignone
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Pino Torinese Gianluigi Bodo
Paola Rossi
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Contents F
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Part I Numerical Methods P
Computational Methods for Hyperbolic Equations
E.F. Toro....................................................... 3
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1 Equations ................................................... 4
2 The Finite Difference Method.................................. 16
3 Two Riemann Solvers: HLLC and EVILIEN....................... 31
4 Non-linear Methods for Scalar Equations ........................ 43
5 Non-linear Schemes for Hyperbolic Systems...................... 55
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References ...................................................... 67
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Shock-Capturing Schemes in Computational MHD
A. Mignone, and G. Bodo......................................... 71
1 Introduction ................E................................. 71
2 The MHD Equations ......................................... 72
3 The Riemann Problem in MHD ................................ 73
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4 The ∇·B =0 Condition ...................................... 91
References ...................................................... 99
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Part II Hydrodynamic and Magneto-Hydrodynamic Instabilities
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The Kelvin–Helmholtz Instability
E. Trussoni .....................................................105
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1 Introduction .................................................105
2 Definitions ..................................................106
3 Equations anNd Mathematical Approach .........................107
4 KHI: Linear Analysis .........................................109
5 KHI: Nonlinear Evolution .....................................121
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6 Conclusions..................................................126
References ......................................................129
VIII Contents
Pressure-Driven Instabilities in Astrophysical Jets
P.-Y. Longaretti .................................................131
1 Introduction .................................................131
2 Heuristic Description of MHD Instabilities.......................133
3 Ideal MHD in Static Columns..............................F....137
4 The Energy Principle and Its Consequences......................140
5 Dispersion Relation in the Large Azimuthal Field Limit ....O.......141
6 Moving Columns .............................................146
7 Summary and Open Issues ....................................147
References ............................................O..........150
Thermal Instabilities
G. Bodo ..........................................R..............153
1 Introduction .................................................153
2 Physical Discussion...........................................154
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3 Linear Analysis ..............................................156
4 Influence of Radiative Losses on the KH Instability ...............160
References .................................. ....................161
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The Oscillatory Instability of Radiative Shock Waves
A. Mignone .....................................................163
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1 Introduction .................................................164
2 Linear Theory ...............................................165
3 Nonlinear Dynamics ...............T...........................171
4 Discussion...................................................174
References ........................C..............................175
Index..........................................................177
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Part I
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Numerical Methods
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