3-Dimensional MHD Simulation of Earth's Magnetosphere
<Example to Execute the MHD Code Using HPF/JA and Graphic Programs>

2001.09.29  by T. Ogino

   We will demonstrate how to execute the 3-Dimensional magnetohydrodynamic 
(MHD) Simulation of Earth's Magnetosphere in 1/4 volume by HPF/JA and how 
to use the graphics programs to make PostScript files and VRML files in 
this section. In the MHD model, MHD and Maxwell's equations are solved in 
the solar-magnetospheric coordinate system by using modified leap-frog 
method when the upstream solar wind and interplanetary magnetic field (IMF) 
boundary conditions are given. Moreover, north-south symmetry and dawn-dusk 
symmetry are assumed, therefore it is enough to solve 1/4 volume as the 
simulation box. The main simulation Fortran program, proghpf.f is fully 
vectorized and fully parallelized by HPF/JA on a vector/parallel-type 
supercomputer, Fujitsu VPP5000/56 in the Computer Center, Nagoya University.  
By executing the main MHD simulation code, a simulated binary file is 
produced as output. When the output binary file is used as input, graphics 
programs can be executed to make PostScript files and VRML files for three 
dimensional visualization. 


 main program : proghpf.f  using  HPF/JA
     proghpf.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 normalization 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 HPF (High Performance Fortran) with 2PE
    HPF Fortran program, proghpf.f is located in directory, test and 
    the compile information is found in the file, hpflist.
    1. qsub -q x -eo -o pconphpf2.out pcomphpf2.sh
       compile "proghpf.f" by parallelization and vectorization mode
    2. qsub -q z -eo -lPv 2 -o pexechpf.out pexechpf.sh
       execute the execution file "proghpf"

       <pcomphpf2.sh>
         cd test
         frt -Wh,-Lt proghpf.f -Pdt -o proghpf -Z hpflist
       <pexechpf.sh>
         #  @$ -lt 1:30:00
         #  @$-q z  -eo
         cd test
         timex proghpf

  where file must be defined in open statement like

c      open(10,file='earthbh0.data',
c    1         access='sequential',form='unformatted')
       open(11,file='earthbh1.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 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).