{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 36 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 258 49 "Satcion\341rius \341ram l\341s akad\341ly mellet 2-dimenzi\363ban" }{TEXT 257 0 "" }}{PARA 257 "" 0 "" {TEXT 259 11 "S.E. Koonin" }{TEXT -1 2 ": " }{TEXT 260 21 "Computational Physics" }{TEXT -1 2 ", " }{TEXT 261 54 "The Benjamin/C ummings Publishing Company, Inc., (1986)" }}{PARA 257 "" 0 "" {TEXT 262 18 "alapj\341n \341tdolgozta" }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 13 "Bartha Ferenc" }}{PARA 257 "" 0 "" {TEXT -1 14 "2002. m \341jus 8." }}{PARA 0 "" 0 "" {TEXT -1 241 "Balr\363l \366sszenyomhata tlan folyad\351k \341ramlik be a szimul\341ci\363s tartom\341nyban. Az akad\341ly hat\341s\341ra kialakul\363 \341raml\341si k\351pet hat \341rozzuk meg. A k\351tdimenzi\363s perem\351rt\351k-probl\351m\341t \+ relax\341ci\363s m\363dszerrel t\341rgyaljuk. R\351szletek a mell\351k elt \372tmutat\363ban...." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart:with(plots):with(linalg):" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Relax Phi procedure" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 80 "RelaxPhi:=proc(psi::array,eta::array,flg::arra y)\nglobal X,Y,wo,wn;\nlocal i,j,t1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for j from 2 to Y-2 do" }{MPLTEXT 0 21 6 "\nLeft:" }{MPLTEXT 1 0 101 " t1:=psi[3,j]+psi[2,j+1]+psi[2,j-1]-eta[2,j]:\n psi[2,j]:= t1/3*wn+wo*psi[2,j]:psi[1,j]:=psi[2,j]:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 "Middle:" }{MPLTEXT 1 0 194 " for i from 3 to X-2 do\n if (flg[i,j]=0) then\n t1:=psi[i+1,j]+psi[i-1,j]+psi[i,j+1]+psi[ i,j-1]-eta[i,j]:\n psi[i,j]:=t1/4*wn+wo*psi[i,j]:\n e nd if:\n end do:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 " Right:" } {MPLTEXT 1 0 117 " t1:=psi[X-2,j]+psi[X-1,j+1]+psi[X-1,j-1]-eta[X-1,j] :\n psi[X-1,j]:=t1/3*wn+wo*psi[X-1,j]:psi[X,j]:=psi[X-1,j]:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "end do: \n " }{MPLTEXT 0 21 4 "Top: " }{MPLTEXT 1 0 164 " for i from 3 to X-2 do\n t1:=psi[i+1,Y-1]+ psi[i-1,Y-1]+psi[i,Y-2]+1-eta[i,Y-1]:\n psi[i,Y-1]:=t1/3*wn+wo*p si[i,Y-1]:psi[i,Y]:=psi[i,Y-1]+1:\n end do:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 "Corner:" }{MPLTEXT 1 0 300 "\nt1:=psi[3,Y-1]+psi[2,Y- 2]+1-eta[2,Y-1]:\npsi[2,Y-1]:=t1/2*wn+wo*psi[2,Y-1]:\npsi[2,Y]:=psi[2, Y-1]+1:psi[1,Y-1]:=psi[2,Y-1]:psi[1,Y]:=psi[2,Y]:\nt1:=psi[X-2,Y-1]+ps i[X-1,Y-2]+1-eta[X-1,Y-1]:\npsi[X-1,Y-1]:=t1/2*wn+wo*psi[X-1,Y-1]:\nps i[X-1,Y]:=psi[X-1,Y-1]+1:psi[X,Y-1]:=psi[X-1,Y-1]:psi[X,Y]:=psi[X-1,Y] :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc:" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "Relax Eta procedure" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "RelaxEta:=proc(psi::array,eta::array,flg::array)\ngl obal X,Y,wo,wn,R4,Hy,Sx,Ex;\nlocal i,j,t1,t2,t3,t4;\n" }{MPLTEXT 0 21 18 "Internal Boundary:" }{MPLTEXT 1 0 225 "\nfor j from 1 to Hy do\n e ta[Sx,j]:=2*psi[Sx-1,j]:\n eta[Ex,j]:=2*psi[Ex+1,j]:\nend do:\neta[Sx, Hy]:=psi[Sx-1,Hy]+psi[Sx,Hy+1]:\neta[Ex,Hy]:=psi[Ex+1,Hy]+psi[Ex,Hy+1] :\nfor i from Sx+1 to Ex-1 do\n eta[i,Hy]:=2*psi[i,Hy+1]:\nend do:\n" }{MPLTEXT 0 21 10 "Main loop:" }{MPLTEXT 1 0 300 "\nfor j from 2 to Y- 1 do\n for i from 2 to X-2 do\n if(flg[i,j]=0) then \n t1:=eta[i+1, j]+eta[i-1,j]+eta[i,j+1]+eta[i,j-1]:\n t2:=(psi[i+1,j]-psi[i-1,j])*( eta[i,j+1]-eta[i,j-1]):\n t3:=(psi[i,j+1]-psi[i,j-1])*(eta[i+1,j]-et a[i-1,j]):\n eta[i,j]:=wn*(t1+R4*(t2-t3))/4+wo*eta[i,j]:\n end if: \n end do:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 6 "Right:" }{MPLTEXT 1 0 279 "\n t1:=eta[X-2,j]+eta[X-1,j+1]+eta[X-1,j-1]:\n t2:=(psi[X,j]- psi[X-2,j])*(eta[X-1,j+1]-eta[X-1,j-1]):\n t3:=-(psi[X-1,j+1]-psi[X- 1,j-1])*eta[X-2,j]:\n t4:=(t1+R4*(t2-t3))/(3+R4*(psi[X-1,j+1]-psi[X- 1,j-1])):\n eta[X-1,j]:=wn*t4+wo*eta[X-1,j]:\n eta[X,j]:=eta[X-1,j ]:\nend do:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "end proc:" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Szimul\341ci\363s doboz: " } {MPLTEXT 1 0 102 "X:=30:Y:=20:\npsi:=array(1..X,1..Y):phi:=array(1..X, 1..Y):\neta:=array(1..X,1..Y):flg:=array(1..X,1..Y):" }{TEXT 0 1 "\n" }{TEXT -1 9 "Akad\341ly: " }{MPLTEXT 1 0 21 "Sx:=12:Ex:=16:Hy:=6:\n" } {TEXT -1 16 "Kezdeti \351rt\351kek\n" }{MPLTEXT 1 0 143 " for i from 1 to X do\n for j from 1 to Y do\n psi[i,j]:=evalf(j-1):phi[i,j]: =0.:\n flg[i,j]:=0:eta[i,j]:=evalf(0):\n end do:\n end do:\n" } {TEXT -1 10 "Az akad\341ly" }{MPLTEXT 1 0 155 "\n for i from Sx to Ex \+ do\n for j from 1 to Hy do\n flg[i,j]:=1:psi[i,j]:=0\n end do: \n end do:\nlistcontplot(psi,view=[1..X,1..Y],levels=10,axes=boxed);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Reynolds sz\341m \351s a kever \351si m\351rt\351k\n" }{MPLTEXT 1 0 49 "R:=0.5:omega:=0.5:\nR4:=R/4:w n:=omega:wo:=1-omega:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Relax \341ci\363s ciklus (T\366bbsz\366r le kell futtatni, mert igen lassan \+ konverg\341l!)\n" }{TEXT 2 0 "" }{TEXT 19 0 "" }{MPLTEXT 1 0 254 "for \+ n from 1 to 20 do\n RelaxPhi(psi,eta,flg):\n delta:=0:\n for i fr om 1 to X do\n for j from 1 to Y do\n delta:=max(delta,abs(psi[ i,j]-phi[i,j])):\n phi[i,j]:=psi[i,j]:\n end do:\n end do:\n \+ print(n,delta);\n RelaxEta(psi,eta,flg):\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "listcontplot(psi,view=[1..X,1..Y],levels= 10,axes=boxed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "ph:=list contplot(phi):pe:=listcontplot(eta):display([ph,pe],view=[1..X,1..Y]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }