3-Dimensional MHD Simulation of Earth's Magnetosphere (English)
(Example to execute the MHD Code and Graphic programs)

 main program : earthb10.f
     earthb10.f  using modified leap-frog scheme
     3D MHD simulation of 1/4 earth's magnetosphere
     Cartesian coordinate   finite resistivity  45 degree boundary


 graphics program to make PostScript files

 1. gm150b.f (main) + gsub150.f (subroutine)
    noon-midnight meridian and equatorial plots (black and white)
 2. gm220b.f (main) + gsub220.f (subroutine)
    energy distribution of cross section
 3. gm480b.f (main) + gsub480.f (subroutine)
    3-dimensional magnetic field lines

 3-dimensional graphics program by VRML files
    

 1. zvrmagb.f (main) + zvrsubb.f (subroutine)
    3-dimensional magnetic field lines
 2. zvrcrob.f (main) + zvrsubb.f (subroutine)
    cross sectional pattern by pixel image


**Summary of parameters in MHD Simulation Code**

(nx,ny,nz)=(180,60,60)        : grid number without boundary
 nxp=30                       : parameter to determine earth position
 last=1024                    : number of time steps
 iiq0=8                       : a unit of modified leap-frog scheme 
 iip0= 32                     : adjust upstream boundary condition
 iis0= 1024                   : sampling step of data
 thx=4.00                     : parameter to adjust time step
 
(xl,yl,zl)=(90.5,30.5,30.5)Re : length in each direction
 hx=xl/float(nx+1)=0.5Re      : grid interval in x direction
 hy=yl/float(ny+1)=0.5Re      : grid interval in y direction
 hz=zl/float(nz+1)=0.5Re      : grid interval in z direction
 t=0.5*hx*thx                 : time interval
 t(real)=t*ts                 : real time to one time step advance
        =0.5*0.5*4.00*0.937   : ts is normalization value in time
        =0.937 sec

 x=0.5*hx*float(2*i-nx2-1+2*nxp) : x position versus grid number
 y=0.5*hy*float(2*j-3)           : y position versus grid number
 z=0.5*hz*float(2*k-3)           : z position versus grid number

  where nx2=nx+2, ny2=ny+2 and nz2=nz+2

 ro01=5.0E-4 (5/cc)           : mass density of solar wind
 pr01=3.56E-8                 : pressure of solar wind
 vsw=0.044   (300km/s)        : speed of solar wind
 bis=CP(11)=1.5E-4 (5nT)      : amplitude of IMF

 eatt                         : resistivity
 rmuu                         : viscosity
 eud0                         : friction or collision term


1-dimensional array variable f(i1)=f(i,j,k,m)

 n1=nx+2,n2=n1*(ny+2),n3=n2*(nz+2)
 nb=8,nbb=11,n4=n3*nb,n5=n3*nbb

 i1=i+n1*(j-1)+n2*(k-1)+n3*(m-1)
 
    m=1  : rho,  plasma density
    m=2  : Vx
    m=3  : Vy
    m=4  : Vz
    m=5  : P,    plasma pressure
    m=6  : Bx
    m=7  : By
    m=8  : Bz


**execution of main program**
1. f77 -O earthb10.f
2. a.out &

  where file must be defined in open statement like

c      open(10,file='earthb10.data',
c    1         access='sequential',form='unformatted')
       open(11,file='earthb11.data',
     1         access='sequential',form='unformatted')
c

or

1. f77 -o earthb10 -O earthb10.f
2. earthb10 &

**execution of PostScript graphics program**

1. f77 -c -O gsub150.f
2. f77 -O gm150b.f gsub150.o
3. a.out > gm150a.ps &
4. gs gm150a.ps
5. lp gm150a.ps

1. f77 -c -O gsub220.f
2. f77 -O gm220b.f gsub220.o
3. a.out > gm220a.ps &

1. f77 -c -O gsub480b.f
2. f77 -O gm480b.f gsub480b.o
3. a.out & : output is written in fort.10

**execution of VRML graphics program**

 1. f77 -c -O zvrsubb.f
 2. f77 -O zvrmagb.f zvrsubb.o
 3. a.out & : output is written in fort.10
 4. mv fort.10 fort.102

 1. f77 -c -O zvrsubb.f
 5. f77 -O zvrcrob.f zvrsubb.o
 6. a.out & : output is written in fort.10
 7. mv fort.10 fort.101
 8. cat fort.101 fort.102 > zvrml01.wrl

References:

T. Ogino, A three-dimensional MHD simulation of the interaction of the solar
    wind with the earth's magnetosphere: The generation of field-aligned
    currents, J. Geophys. Res., 91, 6791-6806 (1986).

T. Ogino, R.J. Walker and M. Ashour-Abdalla, A global magnetohydrodynamic
    simulation of the magnetosheath and magnetopause when the interplanetary
    magnetic field is northward, IEEE Transactions on Plasma Science,
    Vol.20, No.6, 817-828 (1992).

T. Ogino, Two-Dimensional MHD Code, (in Computer Space Plasma Physics),
    Ed. by H. Matsumoto and Y. Omura, Terra Scientific Publishing Company,
    161-215, 411-467 (1993).

T. Ogino, R.J. Walker and M. Ashour-Abdalla, A global magnetohydrodynamic
    simulation of the response of the magnetosphere to a northward turning of
    the interplanetary magnetic field, J. Geophys. Res., Vol.99, No.A6,
    11,027-11,042 (1994).