laxwendroff.f90

laxwendloff算法求解流体力学问题

module define 
  implicit none
  integer,parameter::Nmax=200
  real::dx,dt

  contains
  subroutine initial(u,x)
    implicit none 
	real::u(0:Nmax),x(0:Nmax)
	integer::j

	do j=0,Nmax
	  if(x(j)<=0.2) then
	    u(j)=0.0
	  else if(x(j)>0.2.and.x(j)<=0.5) then
	    u(j)=sin((x(j)-0.2)*10*3.1415926)
	  else if(x(j)>0.5.and.x(j)<=0.7) then
	    u(j)=7.5*(x(j)-0.5)
	  else 
	    u(j)=-1.0
	  end if
    end do
  end subroutine
end module

program main
  use define
  implicit none
  real::x(0:Nmax),u(0:Nmax),u_1(0:Nmax)
  real::lampta,a,T
  integer::j,n,Step
  T=1.0
  dx=1.0/Nmax
  a=0.2
  lampta=0.1
  dt=lampta*dx/a
  Step=int(T/dt)
  do j=0,Nmax
    x(j)=0+dx*j
  end do
  
  call initial(u,x)
  
  do n=1,Step
    do j=1,Nmax-1
      u_1(j)=u(j)-lampta*(u(j+1)-u(j-1))/2.0+lampta**2*(u(j+1)-2*u(j)+u(j-1))/2.0
    end do
	u_1(Nmax)=u_1(Nmax-1)
    u_1(0)=0.0
    u=u_1
	print*,n
  end do
  open(2006,file="u.txt")
  do j=0,Nmax
    write(2006,*)u(j)
  end do
  open(2007,file="x.txt")
  do j=0,Nmax
    write(2007,*)x(j)
  end do
end program