利用MacCormack两部差分格式求解一维激波管问题Fortran程序.doc

! MacCormack1D.for !-!利用MacCormack两部差分格式求解一维激波管问题! !- program MacCormack1D implicit double precision (a-h,o-z) parameter (M=1000) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:M+1,0:2),Uf(0:M+1,0:2) dimension Ef(0:M+1,0:2) GAMMA=1.4 !气体常数 PI=3.1415926 J=M !网格数 dL=2.0 !计算区域 TT=0.4 !总时间 Sf=0.8 !时间步长因子 call Init(U,dx) T=01 dt=CFL(U,dx) T=T+dt write(*,*)T=,T,dt=,dt call MacCormack_1D_Solver(U,Uf,Ef,dx,dt)call bound(U,dx) if(T.lt.TT)goto 1 call Output(U,dx) end!-!计算时间步长!入口: U， 当前物理量，dx, 网格宽度；!返回: 时间步长。!- double precision function CFL(U,dx) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2) dmaxvel=1e-10 do 10 i=1,J uu=U(i,1)/U(i,0) p=(GAMMA-1)*(U(i,2)-0.5*U(i,0)*uu*uu) vel=dsqrt(GAMMA*p/U(i,0)+dabs(uu) if(vel.gt.dmaxvel)dmaxvel=vel10 continue CFL=Sf*dx/dmaxvel end !-!初始化!入口: 无；!出口: U, 已经给定的初始值，dx，网格宽度。!- subroutine Init(U,dx) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2)!初始条件 rou1=1.0 u1=0 v1=0 p1=1.0 rou2=0.125 u2=0 v2=0 p2=0.1 dx=dL/J do 20 i=0,J/2 U(i,0)=rou1 U(i,1)=rou1*u1 U(i,2)=p1/(GAMMA-1)+0.5*rou1*u1*u120 continue do 21 i=J/2+1,J+1 U(i,0)=rou2 U(i,1)=rou2*u2 U(i,2)=p2/(GAMMA-1)+0.5*rou2*u2*u221 continue end!-!边界条件!入口: dx，网格宽度；!出口: U， 已经给定边界。!- subroutine bound(U,dx) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2)!左边界 do 30 k=0,2 U(0,k)=U(1,k)30 continue!右边界 do 31 k=0,2 U(J+1,k)=U(J,k)31 continue end!-!根据U计算E!入口: U，当前U矢量；!出口: E，计算得到的E矢量，! U、E定义见Euler方程组。!- subroutine U2E(U,E,is,in) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2),E(0:J+1,0:2) do 40 i=is,in uu=U(i,1)/U(i,0) p=(GAMMA-1)*(U(i,2)-0.5*U(i,1)*U(i,1)/U(i,0) E(i,0)=U(i,1) E(i,1)=U(i,0)*uu*uu+p E(i,2)=(U(i,2)+p)*uu40 continue end!-!一维 差分格式求解器!入口: U， 上一时刻U矢量，! Uf、Ef，临时变量，! dx，网格宽度，dt,，时间步长；!出口: U， 计算得到得当前时刻U矢量。!- subroutine MacCormack_1D_Solver(U,Uf,Ef,dx,dt) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2),Uf(0:J+1,0:2) dimension Ef(0:J+1,0:2) r=dt/dx dnu=0.25 do 60 i=1,J do 60 k=0,2!开关函数 q=dabs(dabs(U(i+1,0)-U(i,0)-dabs(U(i,0)-U(i-1,0)/(dabs(U(i+1,0)-U(i,0)+dabs(U(i,0)-U(i-1,0)+1e-10)!人工黏性项 Ef(i,k)=U(i,k)+0.5*dnu*q*(U(i+1,k)-2*U(i,k)+U(i-1,k) 60 continue do 61 k=0,2 do 61 i=1,J U(i,k)=Ef(i,k)61 continue call U2E(U,Ef,0,J+1) do 63 i=0,J do 63 k=0,2!U(n+1/2)(i+1/2) Uf(i,k)=U(i,k)-r*(Ef(i+1,k)-Ef(i,k)63 continue !E(n+1/2)(i+1/2) call U2E(Uf,Ef,0,J) do 64 i=1,J do 64 k=0,2!U(n+1)(i) U(i,k)=0.5*(U(i,k)+Uf(i,k)-0.5*r*(Ef(i,k)-Ef(i-1,k) 64 continue end!-!输出结果, 用 数据格式画图!入口: U， 当前时刻U矢量，! dx，网格宽度；!出口: 无。!- subroutine Output(U,dx) implicit double precision (a-h,o-z) common /G_def/ GAMMA,PI,J,JJ,dL,TT,Sf dimension U(0:J+1,0:2) open(1,file=MacCormack_1D result.txt,status=unknown) do 80 i=0,J+1 rou=U(i,0) uu=U