3-Dimensional MHD Simulation of Earth's Magnetosphere

2001.09.29  by T. Ogino


 main program : prog90.f  using  VPP Fortran
     earthb10.f  using modified leap-frog scheme
     3D MHD simulation of 1/4 earth's magnetosphere
     Cartesian coordinate   finite resistivity  45 degree boundary


(nx,ny,nz)=(320,80,80)       : grid number without boundary
 nxp=80                      : parameter to determine earth position
 last=16384                  : number of time steps
 iiq0=8                      : a unit of modified leap-frog scheme 
 iip0= 32                    : adjust upstream boundary condition
 iis0= 8192                  : sampling step of data
 thx=2.3450007               : parameter to adjust time step
 
(xl,yl,zl)=(128.4,32.4,32.4)Re: length in each direction
 hx=xl/float(nx+1)=0.4Re     : grid interval in x direction
 hy=yl/float(ny+1)=0.4Re     : grid interval in y direction
 hz=zl/float(nz+1)=0.4Re     : 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*0.4*2.3450007*0.937  : ts is nornalization value in time
        =0.43945 sec
 Time(iis0)=iis0*t(real)=8192*0.43945=3600(sec)=60(min)=1(hour)

 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


4-dimensional array variable f(i,j,k,m)

 i=[1,nx2], j=[1,ny2], k=[1,nz2], m=[1,nb]
   nb=8
 
    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 in VPP5000>>
  Execution by Fortran90 with 2PE (Vectorization and Parallelization)
    In this case one needs to declare to use 2PE by (npe=2) in
    source program.
    1. qsub -q c -eo -o pcomp90.out pcomp90.sh
       compile "prog90.f" by parallelization and vectorization mode.
    2. qsub -q z -eo -lPv 2 -o pexec90.out pexec90.sh
       execute the execution file "prog90"

<<pcomp90.sh>>
gpcs% more pcomp90.sh
cd sub0
frt -Wx -o prog90 prog90.f

<<pexec90.sh>>
gpcs% more pexec90.sh
#  @$ -lt 9:30:00
#  @$-q z  -eo
cd sub0
timex prog90

  where file must be defined in open statement like

c      open(10,file='earthbv0.data',
c    1         access='sequential',form='unformatted')
       open(11,file='earthbv1.data',
     1         access='sequential',form='unformatted')
c


<<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 zvrsuba.f
 5. f77 -O zvrcrob.f zvrsuba.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).