[FLASH-USERS] 3DMHD +usm, jumps of divb at refinement jumps
Martin Huarte-Espinosa
mh475 at cam.ac.uk
Fri Feb 20 10:59:40 EST 2009
Hi Chris and thanks for your answer. I've tried the following,
unsuccessfully:
./setup /Sysims/mhd_ug_nofbs -3d +usm -auto -opt +nofbs +serialIO
-objdir=mhd_ug_nofbs -site=apgrid && cd mhd_ug_nofbs/ && make
Best,
Martin HE.
On Fri, Feb 20, 2009 at 3:41 PM, Chris Daley <cdaley at flash.uchicago.edu>wrote:
> This is only a response to your first problem. I think FLASH is
> failing to link because your HDF5 build does not have parallel IO
> support. If you would like to use parallel IO, re-build HDF5 with the
> additional configure options "--enable-parallel CC=mpicc". If not,
> then simply add the shortcut +serialIO during FLASH setup for serial IO.
>
> Regards,
> Chris
>
> Martin Huarte-Espinosa wrote:
>
>> Good day Flash community:
>>
>> Two questions. I'll be really thankful if you had any hints about them.
>>
>> 1) I'm trying to complie flash3.1 for a uniform grid with no fixed block
>> size:
>>
>> ./setup mhd_ug_nofbs -3d +usm -auto -opt +nofbs -site=apgrid
>>
>> and I get:
>>
>> /-L/mraosw/data1/mh475/krause/lib/hdf/5-1.6.5-amd-icc/lib -lhdf5 -lz
>> -lhdf5_fortran -L/mraosw/data1/mh475/krause/lib/mpich-1.2.6/lib -lmpich
>> /home/krause/dataw/lib/mpich-1.2.4/lib/libmpich.a(p4_secure.o)(.text+0x91):
>> In function `start_slave':
>> : warning: Using 'getpwuid' in statically linked applications requires at
>> runtime the shared libraries from the glibc version used for linking
>> /mraosw/data1/mh475/krause/lib/hdf/5-1.6.5-amd-icc/lib/libhdf5.a(H5FDstream.o)(.text+0x723):
>> In function `H5FD_stream_open_socket':
>> : warning: Using 'gethostbyname' in statically linked applications
>> requires at runtime the shared libraries from the glibc version used for
>> linking
>> io_h5file_interface.o(.text+0x6d): In function `io_h5init_file_':
>> : undefined reference to `H5Pset_fapl_mpio'
>> io_h5file_interface.o(.text+0x12f): In function
>> `io_h5open_file_for_read_':
>> : undefined reference to `H5Pset_fapl_mpio'
>> make: *** [flash3] Error 1/
>>
>> I've tried, unsuccessfully, to edit some parts of the cluster's
>> Makefile.h.
>>
>>
>> 2) I'm implementing a gas with a random magnetic distribution. I generate
>> the magnetic fields outside flash, making sure their divb~1.e-14. I then
>> read these fields into Flash3.1 and they work well for a uniform grid or
>> with the AMR with lrefine_max=lrefine_min. However, if I give lrefine_max
>> different from lrefine_min, divb appears to be fine at time=0, but after the
>> first timestep it gets jumps up to ~ 0.1 at cells adjacent to refinement
>> jumps only. I'm attaching important bits of info below.
>>
>> Thanks a lot.
>>
>> ./setup MySims/mhd_01 -3d +usm -auto -opt -maxblocks=400 -site=darwin
>>
>> ------------------------
>> /subroutine Simulation_initBlock(blockID, myPE, F) ! following the setup
>> from the Fields loop test problem/
>>
>> / use Simulation_data, ONLY : sim_gCell, sim_gamma, &/
>> / sim_smallX, sim_smallP, &/
>> / sim_beta, sim_B_cluster, &/
>> / sim_killdivb, sim_rc, &/
>> /sim_xMin, sim_xMax, sim_yMin, &/
>> /sim_yMax, sim_zMin, sim_zMax, &/
>> /sim_n_cube/
>>
>> /! use Grid_data, ONLY : gr_nBlockX, gr_nBlockY, gr_nBlockZ/
>>
>> /! use tree, ONLY : lrefine_max, lrefine_min/
>>
>> / use Grid_interface, ONLY : Grid_getBlkIndexLimits, &/
>> / Grid_getCellCoords, &/
>> / Grid_getBlkPtr, &/
>> / Grid_releaseBlkPtr/
>>
>> / use Driver_interface, ONLY : Driver_abortFlash/
>> / /
>> / implicit none/
>>
>> /#include "constants.h"/
>> /#include "Flash.h"/
>>
>> / !!$ Arguments -----------------------/
>> / integer, intent(in) :: blockID, myPE/
>> / !!$ ---------------------------------/
>>
>> / integer :: i, j, k, n, istat, sizeX, sizeY, sizeZ/
>> / integer, dimension(2,MDIM) :: blkLimits, blkLimitsGC/
>> / real :: enerZone, ekinZone, eintZone/
>> / real :: rot, radius, dx, dy, dz, r0, taper, vel_factor/
>> / real, allocatable,dimension(:) :: xCoord,xCoordL,xCoordR,&/
>> / yCoord,yCoordL,yCoordR,&/
>> / zCoord,zCoordL,zCoordR/
>> / real, dimension(MDIM) :: del/
>> / real, pointer, dimension(:,:,:,:) :: solnData, facexData, faceyData,
>> facezData/
>> / real :: xx,yy,zz/
>> /#ifdef FIXEDBLOCKSIZE/
>> / real, dimension(GRID_IHI_GC+1,GRID_JHI_GC+1,GRID_KHI_GC+1) :: Az,Ax,Ay/
>> / //#else /
>> / real, allocatable, dimension(:,:,:) :: Az,Ax,Ay/
>> / //#endif /
>>
>> /logical, save :: once=.true., once2=.true., VecPotA=.true./
>> / integer :: ii, jj, kk/
>> / real :: B0, x_slope, y_slope, z_slope, &/
>> / idl_x_ini, idl_x_end, &/
>> / idl_y_ini, idl_y_end, &/
>> / idl_z_ini, idl_z_end, &/
>> /largestCell, minimumX, maximumX, &/
>> / minimumY, maximumY ,&/
>> / minimumZ, maximumZ, &/
>> / stdev_b, max_b, mean_pres, mean_b, norm_b
>>
>> // real, dimension(3,sim_n_cube,sim_n_cube,sim_n_cube), intent(in)
>> :: F
>> !contains the previously-generated magnetic fields
>> //!!/
>>
>>
>> / ! dump some output to stdout listing the paramters/
>> / if (myPE == MASTER_PE) then/
>> /1 format (1X, 1P, 4(A7, E13.7, :, 1X))/
>> /2 format (1X, 1P, 2(A7, E13.7, 1X), A7, I13)/
>> / endif/
>>
>> / call Grid_getBlkIndexLimits(blockId,blkLimits,blkLimitsGC)/
>>
>> / sizeX = blkLimitsGC(HIGH,IAXIS)-blkLimitsGC(LOW,IAXIS)+1/
>> / sizeY = blkLimitsGC(HIGH,JAXIS)-blkLimitsGC(LOW,JAXIS)+1/
>> / sizeZ = blkLimitsGC(HIGH,KAXIS)-blkLimitsGC(LOW,KAXIS)+1/
>>
>> / allocate(xCoord(sizeX), stat=istat)/
>> / allocate(xCoordL(sizeX),stat=istat)/
>> / allocate(xCoordR(sizeX),stat=istat)/
>>
>> / allocate(yCoord(sizeY), stat=istat)/
>> / allocate(yCoordL(sizeY),stat=istat)/
>> / allocate(yCoordR(sizeY),stat=istat)/
>>
>> / allocate(zCoord(sizeZ), stat=istat)/
>> / allocate(zCoordL(sizeZ),stat=istat)/
>> / allocate(zCoordR(sizeZ),stat=istat)/
>>
>> / xCoord = 0.0/
>> / xCoordL = 0.0/
>> / xCoordR = 0.0/
>>
>> / yCoord = 0.0/
>> / yCoordL = 0.0/
>> / yCoordR = 0.0/
>>
>> / zCoord = 0.0/
>> / zCoordL = 0.0/
>> / zCoordR = 0.0/
>>
>> /#ifndef FIXEDBLOCKSIZE/
>> / if (NDIM == 2) then/
>> / allocate(Ax(sizeX+1,sizeY+1,1),stat=istat)/
>> / allocate(Ay(sizeX+1,sizeY+1,1),stat=istat)/
>> / allocate(Az(sizeX+1,sizeY+1,1),stat=istat)/
>> / // elseif (NDIM == 3) then/
>> / allocate(Ax(sizeX+1,sizeY+1,sizeZ+1),stat=istat)/
>> / allocate(Ay(sizeX+1,sizeY+1,sizeZ+1),stat=istat)/
>> / allocate(Az(sizeX+1,sizeY+1,sizeZ+1),stat=istat)/
>> / // endif/
>> /#endif/
>>
>>
>> / if (NDIM == 3) then/
>> / call Grid_getCellCoords(KAXIS,blockId,CENTER, sim_gCell,zCoord,
>> sizeZ)/
>> / call Grid_getCellCoords(KAXIS,blockId,LEFT_EDGE,
>> sim_gCell,zCoordL,sizeZ)/
>> / call
>> Grid_getCellCoords(KAXIS,blockId,RIGHT_EDGE,sim_gCell,zCoordR,sizeZ)/
>> / endif/
>> / if (NDIM >= 2) then/
>> / call Grid_getCellCoords(JAXIS,blockId,CENTER, sim_gCell,yCoord,
>> sizeY)/
>> / call Grid_getCellCoords(JAXIS,blockId,LEFT_EDGE,
>> sim_gCell,yCoordL,sizeY)/
>> / call
>> Grid_getCellCoords(JAXIS,blockId,RIGHT_EDGE,sim_gCell,yCoordR,sizeY)/
>> / endif/
>>
>> / call Grid_getCellCoords(IAXIS,blockId,CENTER, sim_gCell,xCoord,
>> sizeX)/
>> / call Grid_getCellCoords(IAXIS,blockId,LEFT_EDGE,
>> sim_gCell,xCoordL,sizeX)/
>> / call
>> Grid_getCellCoords(IAXIS,blockId,RIGHT_EDGE,sim_gCell,xCoordR,sizeX)/
>>
>> / call Grid_getDeltas(blockID,del)/
>> / dx = del(1)/
>> / dy = del(2)/
>> / dz = del(3)/
>>
>> /
>> !------------------------------------------------------------------------------/
>> / ! Construct Az at each cell corner/
>> / ! Bx = dAz/dy - dAy/dz/
>> / ! By = dAx/dz - dAz/dx/
>> / ! Bz = dAy/dx - dAx/dy/
>> / Az = 0./
>> / Ax = 0./
>> / Ay = 0.
>>
>> x_ini = 1.
>> y_ini = 1. z_ini = 1.
>> x_end = real(sim_n_cube)
>> y_end = real(sim_n_cube)
>> z_end = real(sim_n_cube)
>> minimumX = sim_xMin - 4.d0*dx
>> minimumY = sim_yMin - 4.d0*dy
>> minimumZ = sim_zMin - 4.d0*dz
>> maximumX = sim_xMax + 4.d0*dx
>> maximumY = sim_yMax + 4.d0*dy
>> maximumZ = sim_zMax + 4.d0*dz /
>> / /
>> / x_slope = (x_end-x_ini)/(maximumX-minimumX)/
>> / y_slope = (y_end-y_ini)/(maximumY-minimumY) /
>> / z_slope = (z_end-z_ini)/(maximumZ-minimumZ) /
>> / /
>> / do k = blkLimitsGC(LOW,KAXIS),blkLimitsGC(HIGH,KAXIS)+1/
>> / do j = blkLimitsGC(LOW,JAXIS),blkLimitsGC(HIGH,JAXIS)+1/
>> / do i = blkLimitsGC(LOW,IAXIS),blkLimitsGC(HIGH,IAXIS)+1/
>>
>>
>> / ! x Coord at cell corner/
>> / if (i <=blkLimitsGC(HIGH,IAXIS)) then/
>> / xx = xCoordL(i)/
>> / else/
>> / xx = xCoordR(i-1)/
>> / endif/
>>
>> / ! y Coord at cell corner/
>> / if (j <=blkLimitsGC(HIGH,JAXIS)) then/
>> / yy = yCoordL(j)/
>> / else/
>> / yy = yCoordR(j-1)/
>> / endif/
>>
>> / ! z Coord at cell corner/
>> / if (k <=blkLimitsGC(HIGH,KAXIS)) then/
>> / zz = zCoordL(k)/
>> / else/
>> / zz = zCoordR(k-1)/
>> / endif/
>>
>>
>> / ii = nint( x_slope*(xx-minimumX)+idl_x_ini ) /
>> / jj = nint( y_slope*(yy-minimumY)+idl_y_ini )/
>> / kk = nint( z_slope*(zz-minimumZ)+idl_z_ini )/
>>
>> /!--------------------------------------------------------------/
>> /if ( (ii.lt.idl_x_ini).or.(ii.gt.idl_x_end).or.&/
>> / (jj.lt.idl_y_ini).or.(jj.gt.idl_y_end).or.& /
>> / (kk.lt.idl_z_ini).or.(kk.gt.idl_z_end) ) &/
>> /call Driver_abortFlash("*** init_block, IDL-Flash coords. error ***")/
>>
>> /!!--------------------------------------------------------------/
>>
>> !Read the outise-fields into flash
>> / Ax(i,j,k) = F(1,ii,jj,kk)/
>> / Ay(i,j,k) = F(2,ii,jj,kk)/
>> / Az(i,j,k) = F(3,ii,jj,kk)/
>> / /
>> / enddo/
>> / enddo/
>> / enddo/
>>
>>
>> /!Initial conditions:/
>>
>> / call Grid_getBlkPtr(blockID,solnData,CENTER)/
>>
>> /#if NFACE_VARS > 0/
>> / if (sim_killdivb) then/
>> / call Grid_getBlkPtr(blockID,facexData,FACEX)/
>> / call Grid_getBlkPtr(blockID,faceyData,FACEY)/
>> / if (NDIM == 3) call Grid_getBlkPtr(blockID,facezData,FACEZ)/
>> / endif/
>> /#endif/
>>
>>
>> / ! Loop over cells within the block./
>> / do k = blkLimitsGC(LOW,KAXIS),blkLimitsGC(HIGH,KAXIS)/
>> / do j = blkLimitsGC(LOW,JAXIS),blkLimitsGC(HIGH,JAXIS)/
>> / do i = blkLimitsGC(LOW,IAXIS),blkLimitsGC(HIGH,IAXIS)/
>>
>> / solnData(SPECIES_BEGIN,i,j,k)=1.0e0-(NSPECIES-1)*sim_smallX/
>> / do n=SPECIES_BEGIN,SPECIES_END/
>> / solnData(n,i,j,k)=sim_smallX/
>> / enddo/
>> / /
>>
>> / solnData(DENS_VAR,i,j,k)= 1./
>> / solnData(PRES_VAR,i,j,k)= solnData(DENS_VAR,i,j,k)/sim_gamma /
>>
>>
>> / solnData(VELX_VAR,i,j,k)= 0.d0/
>> / solnData(VELY_VAR,i,j,k)= 0.d0/
>> / solnData(VELZ_VAR,i,j,k)= 0.d0/
>>
>> / /
>> / /
>>
>> / ! Compute the gas energy and set the gamma-values needed for
>> the EOS/
>> / ekinZone = 0.5 *
>> dot_product(solnData(VELX_VAR:VELZ_VAR,i,j,k),&/
>> /
>> solnData(VELX_VAR:VELZ_VAR,i,j,k))/
>>
>> / ! specific internal energy/
>> / eintZone =
>> solnData(PRES_VAR,i,j,k)/(sim_gamma-1.)/solnData(DENS_VAR,i,j,k)/
>>
>> / ! total specific gas energy/
>> / enerZone = eintZone + ekinZone/
>>
>> / ! Take a limit value/
>> / enerZone = max(enerZone, sim_smallP)/
>>
>> / solnData(ENER_VAR,i,j,k)=enerZone/
>> / solnData(EINT_VAR,i,j,k)=eintZone/
>> / solnData(GAMC_VAR,i,j,k)=sim_gamma/
>> / solnData(GAME_VAR,i,j,k)=sim_gamma/
>>
>>
>>
>> / enddo/
>> / enddo/
>> / enddo/
>>
>>
>> /!! CURL:/
>> / do k = blkLimitsGC(LOW,KAXIS),blkLimitsGC(HIGH,KAXIS)+1/
>> / do j = blkLimitsGC(LOW,JAXIS),blkLimitsGC(HIGH,JAXIS)+1/
>> / do i = blkLimitsGC(LOW,IAXIS),blkLimitsGC(HIGH,IAXIS)+1/
>>
>>
>> / if ( (j <=blkLimitsGC(HIGH,JAXIS)).and.&/
>> / (k <=blkLimitsGC(HIGH,KAXIS)) ) then/
>> / facexData(MAG_FACE_VAR,i,j,k)= -(Ay(i ,j
>> ,k+1)-Ay(i,j,k))/dz &/
>> /+(Az(i ,j+1,k )-Az(i,j,k))/dy/
>> / end if/
>>
>> / if ( (i <=blkLimitsGC(HIGH,IAXIS)).and.&/
>> / (k <=blkLimitsGC(HIGH,KAXIS)) ) then/
>> / faceyData(MAG_FACE_VAR,i,j,k)= (Ax(i ,j
>> ,k+1)-Ax(i,j,k))/dz &/
>> /-(Az(i+1,j ,k )-Az(i,j,k))/dx/
>> / end if/
>>
>> / if ( (j <=blkLimitsGC(HIGH,JAXIS)).and.&/
>> / (i <=blkLimitsGC(HIGH,IAXIS)) ) then/
>> / facezData(MAG_FACE_VAR,i,j,k)= -(Ax(i ,j+1,k
>> )-Ax(i,j,k))/dy &/
>> /+(Ay(i+1,j ,k )-Ay(i,j,k))/dx/
>> / end if/
>> /!N end/
>>
>> / enddo/
>> / enddo/
>> / enddo/
>>
>> / /!!B, DIVB AND MAGP:
>> / do k=blkLimitsGC(LOW,KAXIS),blkLimitsGC(HIGH,KAXIS)/
>> / do j = blkLimitsGC(LOW,JAXIS),blkLimitsGC(HIGH,JAXIS)/
>> / do i = blkLimitsGC(LOW,IAXIS),blkLimitsGC(HIGH,IAXIS)
>>
>> /
>> / solnData(MAGX_VAR,i,j,k) =
>> 0.5*(facexData(MAG_FACE_VAR,i,j,k)+facexData(MAG_FACE_VAR,i+1,j,k))/
>> / solnData(MAGY_VAR,i,j,k) =
>> 0.5*(faceyData(MAG_FACE_VAR,i,j,k)+faceyData(MAG_FACE_VAR,i,j+1,k))/
>> / if (NDIM == 3) then/
>> / solnData(MAGZ_VAR,i,j,k) =
>> 0.5*(facezData(MAG_FACE_VAR,i,j,k)+facezData(MAG_FACE_VAR,i,j,k+1))/
>> / endif/
>>
>>
>> / /
>> / solnData(DIVB_VAR,i,j,k)= &/
>> / (facexData(MAG_FACE_VAR,i+1,j, k ) -
>> facexData(MAG_FACE_VAR,i,j,k))/dx &/
>> / + (faceyData(MAG_FACE_VAR,i, j+1,k ) -
>> faceyData(MAG_FACE_VAR,i,j,k))/dy/
>>
>> / solnData(DIVB_VAR,i,j,k)= solnData(DIVB_VAR,i,j,k) &/
>> / + (facezData(MAG_FACE_VAR,i, j, k+1) -
>> facezData(MAG_FACE_VAR,i,j,k))/dz/
>>
>>
>> / solnData(MAGP_VAR,i,j,k) =
>> .5*dot_product(solnData(MAGX_VAR:MAGZ_VAR,i,j,k),&/
>> /
>> solnData(MAGX_VAR:MAGZ_VAR,i,j,k))/
>>
>>
>> / enddo/
>> / enddo/
>> / enddo/
>>
>>
>>
>> / ! Release pointer/
>> / call Grid_releaseBlkPtr(blockID,solnData,CENTER)/
>>
>> /#if NFACE_VARS > 0/
>> / if (sim_killdivb) then/
>> / call Grid_releaseBlkPtr(blockID,facexData,FACEX)/
>> / call Grid_releaseBlkPtr(blockID,faceyData,FACEY)/
>> / if (NDIM == 3) call Grid_releaseBlkPtr(blockID,facezData,FACEZ)/
>> / endif/
>> /#endif/
>>
>> /deallocate(xCoord)/
>> /deallocate(xCoordL)/
>> /deallocate(xCoordR)/
>> /!/
>> /deallocate(yCoord)/
>> /deallocate(yCoordL)/
>> /deallocate(yCoordR)/
>>
>> /deallocate(zCoord)/
>> /deallocate(zCoordL)/
>> /deallocate(zCoordR)/
>>
>> /#ifndef FIXEDBLOCKSIZE/
>> / deallocate(Az)/
>> / deallocate(Ax)/
>> / deallocate(Ay)/
>> /#endif/
>>
>> /end subroutine Simulation_initBlock/
>>
>> ---------------------------------
>> flash.par:
>>
>>
>> sim_n_cube = 73 #= 64+8guard+1curl
>> nblockx = 1
>> nblocky = 1
>> nblockz = 1
>> lrefine_max = 5
>> lrefine_min = 3
>> refine_var_1 = "velx"
>> nrefs = 2
>>
>> run_comment = "14Feb09-1"
>> log_file = "14Feb09-1.log"
>> basenm = "14Feb09-1-"
>> restart = .false.
>> nend = 10
>> checkPointFileNumber = 1
>> tmax = 4.0
>> checkpointFileIntervalTime = 1.0
>> plotFileIntervalTime = 8.e-4 #2.5e-2
>> dtmax = 0.02 #0.01
>> plotFileNumber = 0
>>
>> sim_beta = 100.0 #Magnetic beta
>>
>> gamma = 1.666666666667
>>
>> geometry = "cartesian"
>>
>> xmin = -0.5
>> xmax = 0.5
>> ymin = -0.5
>> ymax = 0.5
>> zmin = -0.5
>> zmax = 0.5
>> xl_boundary_type = "outflow"
>> xr_boundary_type = "outflow"
>> yl_boundary_type = "outflow"
>> yr_boundary_type = "outflow"
>> zl_boundary_type = "outflow"
>> zr_boundary_type = "outflow"
>>
>> # Simulation (grid, time, I/O) parameters
>>
>> cfl = 0.3
>> dtini = 1.e-12
>> plot_var_1 = "dens"
>> plot_var_2 = "velx"
>> plot_var_3 = "vely"
>> plot_var_4 = "velz"
>> plot_var_5 = "pres"
>> plot_var_6 = "magx"
>> plot_var_7 = "magy"
>> plot_var_8 = "magz"
>> plot_var_9 = "divb"
>> plot_var_10 = "magp"
>>
>> convertToConsvdInMeshInterp = .true.
>>
>> eintSwitch = 1.e-6
>>
>> #MHD:
>> ForceHydroLimit = .false. #(set .true. when using hydro limit B=0)
>> sim_B_cluster = 1.0
>> UnitSystem = "none"
>> resistive_mhd = .false.
>> killdivb = .true.
>>
>> flux_correct = .true.
>>
>> order = 2 #(first / second order scheme)
>> slopeLimiter = "vanLeer" #(minmod, mc, vanLeer, hybrid, limited)
>> LimitedSlopeBeta= 1. # only needed for the limited slope by Toro
>> charLimiting = .true. #(.false. will give primitive limitings)
>> E_modification = .true. #(.false. will use simple arithmetic avg)
>> energyFix = .true. #(.false. will not fix total energy due to
>> div-free magnetic pressure)
>> facevar2ndOrder = .true. #(.false. will give less accurate solution
>> but fast performance)
>>
>> RiemannSolver = "hll"
>> # CTU integrator
>> CTU = .false. #(6-solve CTU scheme, not recommended)
>>
>> # Prolongation method of Facevars
>> prolMethod = "injection_prol" #(injecton_prol, balsara_prol)
>>
>> #ICM initial conditions with a central initial jet /10:
>> smlrho = 1.0e-4 # dens_j/10.
>> smallp = 1.e-3 # ~ min(pres)_ICM/10
>> smalle = 0.00900001 #(1/gamma)/((gamma-1)*1)/10: initial IMC
>> Therm Energy/10
>> #15.0
>> #smallt = 1.000
>>
>> #Total energy minimum limit
>> smallu = 0.000900001 #[(1/gamma)/((gamma-1)*1) + 0.]/10 initial
>> IMC Total Energy/10
>> #15.5 #smallp/((gamma-1)smlrho)+.5(1)
>> #1815.0 #smallp/((gamma-1)smlrho)+.5(vel_j)^2
>>
>> tiny = 1.e-12
>>
>>
>> Best,
>>
>> Martin HE.
>> mh475 at cam.ac.uk <mailto:mh475 at cam.ac.uk>
>>
>
>
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