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2 1 # ls scalar Makefile anime.pro main.f pldt.pro pldtps.pro rddt.pro Fortran Fortran main.f Fortran 1.1 (make) scalar make main.o a.out out.dat # cd scalar # make f77 -c -o main.o main.f main.f: MAIN: f77 -o a.out main.o./a.out write step= 0 time= 0.000E+00 write step= 50 time= 0.125E+02 write step= 100 time= 0.250E+02 ### normal stop ### # ls Makefile anime.pro main.o pldt.pro rddt.pro a.out* main.f out.dat pldtps.pro 1.2 (out.dat) out.dat 1 (jx) (nx) 2 2
3 time step (ns) (time) x (x) (u) 103 Fortran main.f 53, 55, 59 Format # head out.dat 100, 3 0, , , , ( ) 1.3 IDL IDL ( idl IDL (idl) idl # idl IDL IDL Version 5.5 (sunos sparc). (c) 2001, Research Systems, Inc. Installation number: XXXXX. Licensed for use by: XXXXX IDL> (.r rddt) rddt.pro out.dat idl IDL>.r rddt.r run 3
4 1.3.3 (.r pldt) pldt.pro IDL>.r pldt 1: scalar IDL (exit) exit IDL IDL> exit 4
5 2 2.1 FTCS c c solve equation c c ftcs - start >>> do j=1,jx-1 f(j)=0.5*cs*(u(j+1)+u(j)) enddo f(jx)=f(jx-1) do j=2,jx-1 u(j)=u(j)-dt/dx*(f(j)-f(j-1)) enddo u(1)=u(2) u(jx)=u(jx-1) c ftcs - end >>> 2.2 (jx) 5 parameter jx parameter (jx=100) 5
6 2.3 (nstop, nskip) 14 nstop 15 nskip c time control parameters nstop=100 nskip = CFL (safety) CFL 68 (safety) nskip safety c obtain time spacing safety= (.r anime) anime.pro IDL IDL>.r anime nskip 1 anime.pro window anime.pro 6
7 main.f c====================================================================== c array definitions c====================================================================== implicit real*8 (a-h,o-z) parameter (jx=100) dimension x(1:jx),u(1:jx),f(1:jx) c====================================================================== c prologue c====================================================================== c time control parameters nstop=100 nskip = 50 c c initialize counters time = 0.0 ns = 0 nx = nstop/nskip+1 c c Set initial condition c pi=4.*atan(1.0) c grid dx=1.0 x(1)=dx do j=1,jx-1 x(j+1)=x(j)+dx enddo 7
8 c c c c variable do j=1,jx/2 u(j)= 1.0 enddo do j=jx/2+1,jx u(j)= 0.0 enddo velocity cs=1.0 c c Output initial condition c write(6,103) ns,time 103 format (1x, write, step=,i8, time=,e10.3) open(unit=10,file= out.dat,form= formatted ) write(10,100) jx,nx 100 format(i5,,,i5) write(10,101) ns,time 101 format (i5,,,f6.2) do j=1,jx write(10,102) x(j),u(j) enddo 102 format(f5.1,,,f10.7) c====================================================================== c time integration c====================================================================== 1000 continue ns = ns+1 c c obtain time spacing safety=0.25 dt=safety*dx/cs time=time+dt 8
9 c c solve equation c c ftcs - start >>> do j=1,jx-1 f(j)=0.5*cs*(u(j+1)+u(j)) enddo f(jx)=f(jx-1) do j=2,jx-1 u(j)=u(j)-dt/dx*(f(j)-f(j-1)) enddo u(1)=u(2) u(jx)=u(jx-1) c ftcs - end >>> c c data output if (mod(ns,nskip).eq.0) then write(6,103) ns,time write(10,101) ns,time do j=1,jx write(10,102) x(j),u(j) enddo endif if (ns.lt. nstop) goto 1000 close(10) *======================================================================= write(6,*) ### normal stop ### end 9
10 rddt.pro ; rddt.pro openr,1, out.dat readf,1,jx,nx ; define array ns=intarr(nx) t=fltarr(nx) x=fltarr(jx) u=fltarr(jx,nx) ; temporary variables for read data ns_and_t=fltarr(2,1) x_and_u=fltarr(2,jx) for n=0,nx-1 do begin readf,1,ns_and_t readf,1,x_and_u ns(n)=fix(ns_and_t(0,0)) t(n)=ns_and_t(1,0) u(*,n)=x_and_u(1,*) endfor close,1 free_lun,1 x(*)=x_and_u(0,*) delvar,ns_and_t,x_and_u help end 10
11 pldt.pro!x.style=1!y.style=1!p.charsize=1.4 plot,x,u(*,0),xtitle= x,ytitle= u,linest=1,yrange=[-1,3],xrange=[0,100] for n=1,nx-1 do begin oplot,x,u(*,n) oplot,x,u(*,n),psym=4 endfor end anime.pro!x.style=1!y.style=1!p.charsize=1.4 window,xsize=480,ysize=480 xinteranimate,set=[480,480,nx] for n=0,nx-1 do begin plot,x,u(*,n),xtitle= x,ytitle= u,yrange=[-1,3],xrange=[0,100] oplot,x,u(*,n),psym=4 xinteranimate,frame=n,window=0 endfor xinteranimate end 11
12 1 1 (p273 p282) FTCS j =1,...50 u j =1 j =51, u j =0 ν = c t/ x = Lax-Wendroff minmod ( 1.12, 1.10) 1 u n+1 j u t + c u x FTCS =0 (1) = u n j t x (f n j+1/2 f n j 1/2 ) (2) f n j+1/2 = 1 2 (f j+1 + f j )= 1 2 c(u j+1 + u j ) (3) p21 p u 1 u x x 2: Lax-Wendroff
13 2 Burgers 1 Burgers u t + x ( ) u 2 =0 (4) 2 1 ( 1.15, 1.16) p23 f n j+1/2 = 1 2 {( uj u j 2 ) 1 } 2 2 u j+1 + u j (u j+1 u j ) (5) u t = u κ 2 (6) x 2 FTCS cs kappa c variable do j=1,jx u(j)= exp(-(((x(j)-x(jx/2))/5.)**2)) enddo c c kappa kappa=1.0 13
14 14
15 1 CANS Coordinated Astronomical Numerical Software) 2 CANS CANS CANS CANS CANS CANS CANS CANS netcdf netcdf 15
16 4 CANS CANS Lax-Wendroff Roe CIP-MOCCT CANS MPI CANS/MPI CANS 1 CANS1D 2 3 CANS2D, CANS3D 5 CANS Makefile Makefile cans1d/ CANS 1D (1 ) Fortran cans2d/ CANS 2D (2 ) Fortran cans3d/ CANS 3D (3 ) Fortran cansnc/ netcdf idl/ IDL cans-1.0 cans3d 6 CANS Web CANS 16
17 1 CANS 1D CANS 1D Lax-Wendroff hdmlw # ls hdmlw Makefile mlw_ht.f mlw_m3_g.f mlw_m_g.f mlwfull.f README mlw_ht_c.f mlw_m3t.f mlw_mt.f mlwhalf.f Readme.tex mlw_ht_cg.f mlw_m3t_c.f mlw_mt_c.f mlwsrcf.f mlw_a.f mlw_ht_g.f mlw_m3t_cg.f mlw_mt_cg.f mlwsrch.f mlw_h.f mlw_m.f mlw_m3t_g.f mlw_mt_cgr.f mlw_h_c.f mlw_m3.f mlw_m_c.f mlw_mt_g.f mlw_h_cg.f mlw_m3_c.f mlw_m_cg.f mlw_rh.f mlw_h_g.f mlw_m3_cg.f mlw_m_cgr.f mlwartv.f ( ) md # ls md_shktb Makefile bnd.f pldt.pro README cipbnd.f rddt.pro Readme.pdf main.f shktb_analytic.pro Readme.tex main.pro anime.pro model.f Fortran Fortran.f Fortran README Readme.pdf HTML htdocs web browser Web 17
18 1.1 (make) cans1d cansnc 2 make cans1d make libcans1d.a cansnc make libcansnc.a # cd cans1d # make cd hdmlw; make f77 -O -c mlwfull.f ( ) touch.update # cd../cansnc # make ( ) cans1d cansnc make cans1d cans2d cans3d cansnc 18
19 1.2 (make) make (md shktb) out.cdf # cd md_shktb # make f77 -O -c main.f f77 -O -c model.f f77 -O -c bnd.f f77 -O -c cipbnd.f f77 -o a.out main.o model.o bnd.o cipbnd.o -L.. -lcans1d -L/usr/local/netcdf/lib -lnetcdf./a.out write step= 0 time= 0.000E+00 nd = 1 write step= 75 time= 0.505E-01 nd = 2 write step= 154 time= 0.100E+00 nd = 3 write step= 221 time= 0.142E+00 nd = 4 stop step= 221 time= 0.142E+00 ### normal stop ### 1.3 IDL IDL ( idl IDL (idl) idl # idl IDL IDL Version 5.5 (sunos sparc). (c) 2001, Research Systems, Inc. Installation number: XXXXX. Licensed for use by: XXXXX IDL> 19
20 1.3.2 (.r rddt) rddt.pro.r run IDL>.r rddt help IDL> help ( ) FILE STRING = out.cdf GM FLOAT = IX LONG = 208 NX LONG = 4 PR FLOAT = Array[208, 4] PR1 FLOAT = RO FLOAT = Array[208, 4] RO1 FLOAT = T FLOAT = Array[4] TE FLOAT = Array[208, 4] VX FLOAT = Array[208, 4] X FLOAT = Array[208] Compiled Procedures: $MAIN$ NCGETO1 NCGETOS NCGETS1 NCGETSS ( ) PR( ) RO( ) TE( ) VX( ) 2 ( ) X( ) T( ) 1 help idl PR pr (.r pldt) pldt.pro IDL>.r pldt 20
21 3: md shktb (.r anime) idl anime.pro anime.pro IDL>.r anime IDL (exit) exit IDL 7 IDL> exit 21
22 1 1. (md itshktb) IDL rddt.pro pldt.pro 2. (md shktb) 3. (md shkform) anime.pro 4. MHD (md mhdshktb) 4: md mhdshktb Fortran make out.cdf out1.cdf out.cdf make clean 22
23 2 CANS 1D 3 main.f, model.f, bnd.f md *** # cp -r md_shktb md_shktb1 2.1 (main.f) main.f (ix) (md shktb) (ix) main.f # cd md_shktb # ls Makefile bnd.o model.o README cipbnd.f out.cdf Readme.pdf cipbnd.o pldt.pro Readme.tex main.f rddt.pro a.out* main.o shktb_analytic.pro anime.pro main.pro bnd.f model.f main.f (1 5 ) c====================================================================== c array definitions c====================================================================== implicit real*8 (a-h,o-z) parameter (ix=207) make
24 2.1.2 (tend, dtout) (tend) (dtout) main.f (26 32 ) c c time control parameters c nstop : number of total time steps for the run dtout=0.05 tend= nstop= (md shktb) 24
25 2.2 (model.f) model.f model.f (ro) (vx, vy) (pr) (bx, by) γ (gm) Sedov γ (gm) model.f model.f (13 16 ) c c parameters c gm=5./3. 5./3. 7./5. gm=7./5. make idl :Sedov (md sedov) 25
26 2.3 (main.f) Roe MHD (md mhdshktb) Roe main.f (120 ) c solve hydrodynamic equations c hdmlw - start >>> call mlw_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,dxm,ix) c hdmlw - end <<< c hdroe - start >>> c call roe_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,ix) c hdroe - end <<< c hdcip - start <<< c call cip_m(ro,pr,vx,vy,by,te,vxm,rodx,tedx,vxdxm,vydx c &,bx,bxm,dt,gm,dx,dxm,ix) c hdcip - end <<< mlw m Lax-Wendroff MHD roe m Lax-Wendroff MHD call mlw m call roe m c solve hydrodynamic equations c hdmlw - start >>> c call mlw_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,dxm,ix) c hdmlw - end <<< c hdroe - start >>> call roe_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,ix) c hdroe - end <<< c hdcip - start <<< c call cip_m(ro,pr,vx,vy,by,te,vxm,rodx,tedx,vxdxm,vydx c &,bx,bxm,dt,gm,dx,dxm,ix) c hdcip - end <<< 26
27 2.3.2 CIP MHD (md mhdshktb) CIP Roe main.f CIP 3 CIP hdcip c hdcip - start >>> dimension te(ix),vxm(ix),rodx(ix),tedx(ix),vxdxm(ix),vydx(ix) c hdcip - end <<< c hdcip - start >>> call ciprdy_m(te,vxm,rodx,tedx,vxdxm,vydx,ro,pr,vx,vy &,gm,dx,dxm,ix) call cipbnd(margin,ro,te,vxm,vy,by,rodx,tedx,vxdxm,vydx,ix) c hdcip - end <<< c c solve hydrodynamic equations c hdmlw - start >>> c call mlw_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,dxm,ix) c hdmlw - end <<< c hdroe - start >>> c call roe_m(ro,pr,vx,vy,by,bx,bxm,dt,gm,dx,ix) c hdroe - end <<< c hdcip - start <<< call cip_m(ro,pr,vx,vy,by,te,vxm,rodx,tedx,vxdxm,vydx &,bx,bxm,dt,gm,dx,dxm,ix) c hdcip - end <<< call bnd(margin,ro,pr,vx,vy,by,ix) c floor=1.d-9 c call chkdav(n_floor,ro,vx,floor,ix) c call chkdav(n_floor,pr,vx,floor,ix) c hdcip - start <<< call cipbnd(margin,ro,te,vxm,vy,by,rodx,tedx,vxdxm,vydx,ix) c hdcip - end <<< 27
28 2.4 (bnd.f) bnd.f md shktb bnd.f call bdsppx(0,margin,ro,ix) call bdsppx(0,margin,pr,ix) call bdspnx(0,margin,vx,ix) call bdsppx(1,margin,ro,ix) call bdsppx(1,margin,pr,ix) call bdspnx(1,margin,vx,ix) bdsppx bdspnx bdsppx bdspnx bdsppx(,,, ) margin margin Lax-Wendroff 1 Roe 2 CIP 4 3 (ro) (pr) (vx) bdspnx bdsppx 4 bc/readme 28
29 CANS 1D (cans-1.0 ) hdmlw/ hdroe/ hdcip/ MHD Lax-Wendroff Roe CIP bc/ common/ cndsor/ 1 Red Black SOR cndbicg/ 1 BICG htcl/ selfg/ md_***/ README md_***/readme md_***/readme.pdf PDF md_***/readme.ps PS 29
30 md_advect/ [ ] md_shktb/ [ ] md_shkform/ [ ] md_strongshk/ [ ] md_itshktb/ [ ] md_mhdshktb/ MHD [MHD] md_itmhdshktb/ MHD [ MHD] md_awdecay/ Alfven [ 3 MHD] md_sedov/ Sedov [ ] md_thinst/ [ ] md_cndtb/ [ ] md_cndsp/ [ ] md_spicule/ [MHD ] md_wind/ Parker [ ] md_mhdwind/ MHD Weber-Davis [MHD ] md_diskjet/ MHD [MHD ] md_flare/ [ ] md_cloud/ [ ] md_clsp/ [ ] md_relshk/ [ ] bdcnsx qq(1)=q0 bdfrex qq(1)=qq(2) bdfrdx qq(1)=qq(2)-dqq(2)*dx bdperx qq(1)=qq(ix) bdsppx qq(1)= qq(2) bdspnx qq(1)=-qq(2) bdsmpx qq(1)= qq(3) bdsmnx qq(1)=-qq(3) 30
31 1 CANS 2D, 3D CANS 2D CANS 3D CANS 1D MPI Fortran mdp CANS 1D 1.1 (make) cans2d cansnc make cans2d make libcans2d.a # cd cans2d # make cd hdmlw; make f77 -c mlwfull.f mlwfull.f: mlwfull: f77 -c mlwhalf.f mlwhalf.f: mlwhalf: ( ) CANS 1D cansnc make libcansnc.a ( CANS 1D ) # cd../cansnc # make ( ) 31
32 CANS 3D cans3d make libcans3d.a # cd cans3d # make cd hdmlw; make f77 -c mlwfull.f mlwfull.f: mlwfull: f77 -c mlwhalf.f mlwhalf.f: mlwhalf: ( ) CANS 1D cans1d cans2d cans3d cansnc make 32
33 1.2 (make) make Kelvin-Helmholtz (md kh) # cd md_kh # make f77 -c main.f main.f: MAIN: f77 -c model.f model.f: model: f77 -c bnd.f bnd.f: bnd: f77 -o a.out main.o model.o bnd.o \ -L../.. -lcans2d -lcansnc -L/usr/local/netcdf/lib -lnetcdf./a.out write step= 0 time= 0.000E+00 nd = 1 write step= 83 time= 0.100E+01 nd = 2 write step= 167 time= 0.201E+01 nd = 3 write step= 251 time= 0.301E+01 nd = 4 write step= 336 time= 0.401E+01 nd = 5 write step= 421 time= 0.500E+01 nd = 6 write step= 510 time= 0.600E+01 nd = 7 write step= 605 time= 0.701E+01 nd = 8 write step= 707 time= 0.801E+01 nd = 9 write step= 817 time= 0.900E+01 nd = 10 write step= 940 time= 0.100E+02 nd = 11 stop step= 940 time= 0.100E+02 ### normal stop ### CANS 2D CANS 1D 33
34 1.3 IDL IDL (idl) idl # idl (.r rddt) IDL>.r rddt (.r pldt) IDL>.r pldt % Compiled module: $MAIN$. Plot columns \& rows? : 2,2 Variable for color-maps? (ro,pr,te) : ro start step? : ro pr te (vx, vy, vz) (bx, by, bz) (.r anime) IDL>.r anime 34
35 1.3.5 (loadct,39 xloadct) loadct,39 pldt.pro IDL> loadct,39 loadct B-W Linear( ) 39 rainbow+white( + ) xloadct IDL> xloadct IDL (exit) IDL IDL> exit 35
36 CANS 2D (cans-1.0 ) hdmlw/ MHD Lax-Wendroff bc/ common/ cndsor/ 1 Red Black SOR cndbicg/ 1 BICG htcl/ selfgmg/ Multigrid Iteration commonmpi/ (MPI) cndsormpi/ 1 Red Black SOR (MPI) nccat/ NetCDF md_***/ [ ] mdp_***/ [ ] ( ) md shktb mdp shktb 36
37 md_advect/ [ ] md_shktb/ [ ] md_itshktb/ [ ] md_mhdshktb/ MHD [MHD] md_itmhdshktb/ MHD [ MHD] md_mhd3shktb/ 3 MHD [3 MHD] md_awdecay/ Alfven [ 3 MHD] md_thinst/ [ ] md_cndtb/ [ ] md_mhdcndtb/ MHD [MHD ] md_shkref/ [ ] md_kh/ Kelvin-Helmholtz [ ] md_rt/ Rayleigh-Taylor [ ] md_sndwave/ [ ] md_mhdwave/ MHD [MHD] md_mhdkh/ MHD Kelvin-Helmholtz [MHD] md_mhd3kh/ 3 MHD Kelvin-Helmholtz [3 MHD] md_recon/ [MHD ] md_recon3/ 3 [3 MHD ] md_efr/ Parker [MHD ] md_corjet/ [MHD ] md_mri/ [MHD Coriolis ] md_mricyl/ [MHD Coriolis ] md_reccnd/ [MHD ] md_cndsp/ [ ] md_sedov/ Sedov [ ] md_jetprop/ [ ] md_mhdsn/ MHD [MHD ] md_diskjet/ [MHD ] md_cme/ Low [MHD ] md_cloud/ [ ] md_mhdcloud/ MHD [ MHD ] md_mhdgwave/ MHD [MHD] md_parker/ Parker [MHD ] Version 3.2 (2003/08/08) 37
( ) 1
( ) 1 1 # ls scalar Makefile anime.pro main.f pldt.pro pldtps.pro rddt.pro Fortran Fortran main.f Fortran 1.1 (make) scalar make main.o a.out out.dat # cd scalar # make f77 -c -o main.o main.f main.f:
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Microsoft Word - 03-数値計算の基礎.docx
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情報活用資料
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 21 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 22 L A x y A L x 23 ls -l gnuplot gnuplot> plot "sine.dat"
Microsoft Word - 資料 docx
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 29 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 30 L A x y A L x 31 plot sine curve program sine implicit
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joho09.ppt
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気象観測データの解析 1 AMeDAS データの解析 研究を進めるにあたって データ解析用のプログラムを自分で作成する必要が生じることがあります ここでは 自分で FORTRAN または C でプログラムを作成し CD-ROM に入った気象観測データ ( 気象庁による AMeDAS の観測データ ) を読みこんで解析します データを読みこむためのサブルーチンや関数はあらかじめ作成してあります それらのサブルーチンや関数を使って自分でプログラムを書いてデータを解析していきます
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