MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

MHD Simulation of An Isothermal Sphere

Presented by: Li Shan WengSupervisor: Anthony Allen

August, 8, 2002

© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Introduction

Isothermal Sphere --- the reason

MHD-Magneto Hydrodynamics --- the method

ZEUS 2D Code --- the tool

Simulation --- the thing

Comparison w/ Previous Result --- the justification

Conclusion --- the end

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Isothermal Sphere

Low mass star form in the dense cores of molecular cloud

Other factors of supporting cores against self-gravity collapse

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Isothermal Sphere

Equations governing the collapse of singular isothermal sphere

initial setup:

)(2

),(2

2

RGr

ar )(

4),(

2/1

2

G

rar

0v 0 1)( R

Mg %5.0101masspoint 31

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

ZEUS 2D Code

A two-dimensional code for solving the equations of astrophysical fluid dynamics

ZEUS has a wide variety simulation effects in AFD

The code is applicable to different simulation coordinates

It is used to solve MHD equations for our simulation

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

(M)HD-Magneto Hydrodynamics

Non-relativistic moving frame equations of MHD solved in ZEUS 2D code:

0 vDt

D

BJc

pDt

Dv

1

vpe

Dt

D)(

Ect

B

vtDt

D

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

ZEUS 2D Code

Grid: cylindrical vs. spherical

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Simulation

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Simulation

begin

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Simulation

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Simulation

end

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Comparison with Previous Result

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Comparison with Previous Result

MHD Simulation of An Isothermal Sphere© 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

Conclusion

Frank Shu was right

ZUES2D in spherical coordinates is suitable for isothermal sphere

ZUES2D in spherical coordinates may be suitable for isothermal toroid

Future work on magnetic cases