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gzb1220新蟲(chóng) (小有名氣)
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[求助]
二維菲克定律微分方程求解？ 已有1人參與
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微分方程如圖，如何求解呢？擴(kuò)展到三維又如何求解呢？ 111.jpg |
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onesupeng
金蟲(chóng) (職業(yè)作家)
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【答案】應(yīng)助回帖
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!============================================================= !==LBM for convective-diffusion equation=================================== !==\partial T /\partial t =(\partial^2 T /\partial x^2+ \partial^2 T /\partial y^2) !========Initally developed by Onesupeng================================ !============================2010.2.2=========================== !============================================================= program main include "./para.dat" real*8::T1(nx,ny),T2(nx,ny),T3(nx,ny),Tnp1(nx,ny),Tnm1(nx,ny),right1(nx,ny),right2(nx,ny) integer::i,j,nstep,nplot,ntime character*8::title PI=4.0*atan(1.0) ! kappa=0.05 dx=Lx/(Nx-1) dy=Ly/(Ny-1) do i=1,Nx do j=1,Nx x(i,j)=0.0+(i-1)*dx y(i,j)=0.0+(j-1)*dy right1(i,j)=0.0 right2(i,j)=0.0 V(i,j)=0.0d0 U(i,j)=0.0d0 enddo enddo ds=2.0*PI/Ns do i=1,ns xs(i)=Lx/2+cos(2*PI/ns*(i-1)) ys(i)=Ly/2+sin(2*PI/ns*(i-1)) enddo dt=0.00001 timestop=5.0 Nplot=100 nstep=1 open(unit=1,file='./Init/Init.dat') write(1,*)'variables= "x" "Y"' write(1,*)'ZONE F=POINT I=',Nx,' J=',Ny do j=1,ny do i=1,nx write(1,*)x(i,j),y(i,j) enddo enddo write(1,*)'variables= "x" "Y"' write(1,*)'ZONE F=POINT I=',Ns,' J=',1 do i=1,ns write(1,*)xs(i),ys(i) enddo close(1) !stop ! nstep=0 do while(dt*nstep.LE.timestop) nstep=nstep+1 if(mod(nstep,10).eq.0)write(*,*)"nstep=",nstep do i=1,ns Tb(i)=1.0d0 enddo !call ACTION1 do i=1+1,nx-1 do j=1+1,ny-1 right2(i,j)=right1(i,j) right1(i,j)=(Tn(i+1,j)-2.0*Tn(i,j)+Tn(i-1,j))/dx**2+(Tn(i,j+1)-2.0*Tn(i,j)+Tn(i,j-1))/dy**2 enddo enddo if(Nstep.eq.1)then do i=1+1,nx-1 do j=1+1,ny-1 Tnp1(i,j)=Tn(i,j)+right1(i,j)*dt enddo enddo else do i=1+1,nx-1 do j=1+1,ny-1 Tnp1(i,j)=Tn(i,j)+0.5*(3*right1(i,j)-right2(i,j))*dt enddo enddo endif do i=1,nx Tnp1(i,1)=1.0 !Tnp1(i,2) Tnp1(i,ny)=Tnp1(i,ny-1) enddo do j=1,ny Tnp1(1,j)=Tnp1(2,j) Tnp1(nx,j)=Tnp1(nx-1,j) enddo do i=1,nx do j=1,ny Tnm1(i,j)=Tn(i,j) Tn(i,j)=Tnp1(i,j) enddo enddo if(mod(nstep,nplot).eq.0)then write(title,'(i8.8)')nstep open(unit=1,file='./Out/out'//title//'.dat') write(1,*)'variables= "x" "Y" "T"' write(1,*)'ZONE F=POINT I=',Nx,' J=',Ny do j=1,ny do i=1,nx write(1,*)x(i,j),y(i,j),Tn(i,j) enddo enddo write(1,*)'variables= "x" "Y" "Tn(i,j)"' write(1,*)'ZONE F=POINT I=',Ns,' J=',1 do i=1,ns write(1,*)xs(i),ys(i),F(i) enddo close(1) endif enddo !do end |
3樓2014-01-28 06:55:19
onesupeng
金蟲(chóng) (職業(yè)作家)
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【答案】應(yīng)助回帖
★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感謝參與，應(yīng)助指數(shù) +1
ben_ladeng: 金幣+2, 請(qǐng)耐心等待樓主評(píng)分 2014-01-30 08:22:13
gzb1220: 金幣+10, ★★★很有幫助, 謝謝，這段程序是不是通過(guò)差分法解出來(lái)的？ 2014-02-02 07:55:05
1592203609: 仿真EPI+1 2014-02-22 17:04:33
感謝參與，應(yīng)助指數(shù) +1
ben_ladeng: 金幣+2, 請(qǐng)耐心等待樓主評(píng)分 2014-01-30 08:22:13
gzb1220: 金幣+10, ★★★很有幫助, 謝謝，這段程序是不是通過(guò)差分法解出來(lái)的？ 2014-02-02 07:55:05
1592203609: 仿真EPI+1 2014-02-22 17:04:33
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方程的這個(gè)寫(xiě)法第一次看到，希望我理解的是對(duì)的，擴(kuò)散方程 數(shù)值技術(shù)上說(shuō)，如果是結(jié)構(gòu)網(wǎng)格很容易就得到結(jié)果，下面是Fortran程序，希望對(duì)你有用。一共兩個(gè)文件，main.f90和para.dat。你準(zhǔn)備好之后在目錄下建立Out和Init，即可編譯運(yùn)行。結(jié)果在Out里面，用Tecplot可以直接查看 !main.f90 !================================================================== !==FDM diffusion equation====================================== !==\partial T /\partial t =(\partial^2 T /\partial x^2+ \partial^2 T /\partial y^2) !========Initally developed by onesupeng=================================== !==============2010.2.2========================================= !========================================================== program main include "./para.dat" real*8::T1(nx,ny),T2(nx,ny),T3(nx,ny),Tnp1(nx,ny),Tnm1(nx,ny),right1(nx,ny),right2(nx,ny) integer::i,j,nstep,nplot,ntime character*8::title PI=4.0*atan(1.0) !ÏÂÃæÊDzÎÊý kappa=0.05 dx=Lx/(Nx-1) dy=Ly/(Ny-1) do i=1,Nx do j=1,Nx x(i,j)=0.0+(i-1)*dx y(i,j)=0.0+(j-1)*dy right1(i,j)=0.0 right2(i,j)=0.0 V(i,j)=0.0d0 U(i,j)=0.0d0 enddo enddo ds=2.0*PI/Ns do i=1,ns xs(i)=Lx/2+cos(2*PI/ns*(i-1)) ys(i)=Ly/2+sin(2*PI/ns*(i-1)) enddo dt=0.00001 timestop=5.0 Nplot=100 nstep=1 open(unit=1,file='./Init/Init.dat') write(1,*)'variables= "x" "Y"' write(1,*)'ZONE F=POINT I=',Nx,' J=',Ny do j=1,ny do i=1,nx write(1,*)x(i,j),y(i,j) enddo enddo write(1,*)'variables= "x" "Y"' write(1,*)'ZONE F=POINT I=',Ns,' J=',1 do i=1,ns write(1,*)xs(i),ys(i) enddo close(1) !stop !ʱ¼äÑ­»µ¿ªÊ¼ nstep=0 do while(dt*nstep.LE.timestop) nstep=nstep+1 if(mod(nstep,10).eq.0)write(*,*)"nstep=",nstep do i=1,ns Tb(i)=1.0d0 enddo !call ACTION1 do i=1+1,nx-1 do j=1+1,ny-1 right2(i,j)=right1(i,j) right1(i,j)=(Tn(i+1,j)-2.0*Tn(i,j)+Tn(i-1,j))/dx**2+(Tn(i,j+1)-2.0*Tn(i,j)+Tn(i,j-1))/dy**2 enddo enddo if(Nstep.eq.1)then do i=1+1,nx-1 do j=1+1,ny-1 Tnp1(i,j)=Tn(i,j)+right1(i,j)*dt enddo enddo else do i=1+1,nx-1 do j=1+1,ny-1 Tnp1(i,j)=Tn(i,j)+0.5*(3*right1(i,j)-right2(i,j))*dt enddo enddo endif do i=1,nx Tnp1(i,1)=1.0 !Tnp1(i,2) Tnp1(i,ny)=Tnp1(i,ny-1) enddo do j=1,ny Tnp1(1,j)=Tnp1(2,j) Tnp1(nx,j)=Tnp1(nx-1,j) enddo do i=1,nx do j=1,ny Tnm1(i,j)=Tn(i,j) Tn(i,j)=Tnp1(i,j) enddo enddo if(mod(nstep,nplot).eq.0)then write(title,'(i8.8)')nstep open(unit=1,file='./Out/out'//title//'.dat') write(1,*)'variables= "x" "Y" "T"' write(1,*)'ZONE F=POINT I=',Nx,' J=',Ny do j=1,ny do i=1,nx write(1,*)x(i,j),y(i,j),Tn(i,j) enddo enddo write(1,*)'variables= "x" "Y" "Tn(i,j)"' write(1,*)'ZONE F=POINT I=',Ns,' J=',1 do i=1,ns write(1,*)xs(i),ys(i),F(i) enddo close(1) endif enddo !do end !para.dat implicit none integer,parameter::Nx=201,Ny=201 integer,parameter::Ns=314 real*8,parameter::Lx=10.0d0,Ly=10.0d0 real*8::kappa,PI real*8::dt,timestop,dx,dy,ds real*8::x(nx,ny),y(nx,ny),U(nx,ny),V(nx,ny),Fib(nx,ny) real*8::xs(ns),ys(ns),F(ns),Tb(NS) real*8::Tn(nx,ny) common/para/kappa,PI,dt,timestop,dx,dy,ds common/field/x,y,U,V,Fib,Tn common/lag/xs,ys,F,Tb |
2樓2014-01-28 06:52:38
gzb1220
新蟲(chóng) (小有名氣)
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4樓2014-02-02 07:58:38
onesupeng
金蟲(chóng) (職業(yè)作家)
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5樓2014-02-02 09:50:24
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