mhd simulation of an isothermal sphere © 2002, summer student program, institute of astronomy and...
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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