2. 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 Weng Supervisor: Anthony Allen August, 8, 2002 © 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica

3. 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

4. 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

5. 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:

6. 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

7. 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:

8. MHD Simulation of An Isothermal Sphere © 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica ZEUS 2D Code Grid: cylindrical vs. spherical

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

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

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

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

13. MHD Simulation of An Isothermal Sphere © 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica Comparison with Previous Result

14. MHD Simulation of An Isothermal Sphere © 2002, Summer Student Program, Institute of Astronomy and Astrophysics, Academia Sinica Comparison with Previous Result

15. 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