[drudox]

Hi everybody !! I just wrote a fortran 95 code for solving the burger equations !

      MODULE PARAM 
        IMPLICIT NONE 
        INTEGER, PARAMETER  :: SP = KIND(1.0)
        INTEGER, PARAMETER  :: DP = KIND(1.D0)
      END MODULE 
!-----------------------------------------------------------------------
      MODULE BURGER_2
       USE PARAM 
       IMPLICIT NONE
       
       REAL(DP), PARAMETER   :: x0=0. , xF= 5.
       REAL(DP), PARAMETER   :: t0=0. , tF= 1.0
       REAL(DP), PARAMETER   :: dx=0.001, dt=0.1
       INTEGER , PARAMETER   :: N= CEILING((xF-x0)/dx)
       INTEGER , PARAMETER   :: M= CEILING((tF-t0)/dt)
       REAL(DP), PARAMETER   :: nu = 2D-4 
       REAL(DP), PARAMETER   :: pi=3.14159265358979323846 


      CONTAINS 
!-----------------------------------------------------------------------
         SUBROUTINE BURGER_EXPLICIT (x,t,u) 
           USE PARAM 
           REAL(DP), DIMENSION(N+1)     :: x
           REAL(DP), DIMENSION(M+1)     :: t
           REAL(DP), DIMENSION(N+1,M+1) :: U
           REAL(DP)   :: r,k , CFL
           INTEGER    :: i,j,stat
            
           CFL = DT/DX**2
           Print '(A, F20.5)', 'CFL = ' , CFL
          
           x(1:N+1)       = (/ ( x0+dx*(i-1) , i=1,N+1 ) /)       
           t(1:M+1)       = (/ (t0+ dt*(j-1) , j=1,M+1 ) /)
           U(1:N+1,1:M+1) = RESHAPE((/(((sin(2*pi*(i-1)/N)), i=1,N+1), j=1,M+1)/),(/N+1,M+1/)) 
           !U(1:N+1,1:M+1) = RESHAPE((/(((i), i=1,N+1), j=1,M+1)/),(/N+1,M+1/)) 
           !U(1:N+1,1:M+1) = RESHAPE((/((((     )), i=1,N+1), j=1,M+1)/),(/N+1,M+1/)) 
           
           !DO i=1,N+1
           ! IF (x(i) .LE. 

           !END DO




           !U(1,:)   = x0
           !U(N+1,:) = xF

           !U(:,1)   = t0
           !U(:,M+1) = tF
           


           r = nu*DT/DX**2
           k = DT/(2*DX)
           
           OPEN(10,file='bur2.dat',STATUS='UNKNOWN',IOSTAT=stat)
           DO J=2,M
            DO I=2,N
              U(i,j+1) = r*u(i+1,j)+(1-2*r)*u(i,j)+r*u(i-1,j) - k*u(i,j)*(u(i+1,j)-u(i-1,j))
            END DO
           END DO 
              !IF(J .EQ. 4) THEN
              
              !WRITE(10,FMT='(2F20.5)') x(i), u(i,4)        !((u(i,j) , i=1,N+1), J=1,M+1)
              !END IF 

           OPEN(10,file='bur1.dat',STATUS='UNKNOWN',IOSTAT=stat)
            IF (STAT .NE. 0) THEN 
             WRITE(6,FMT='(A)')'Error opening File ''bur1.dat'' (EXIT1)'
             STOP 
            ELSE     
           DO j=1,M+1  
              WRITE(10,FMT='(3F20.5)') (x(i), t(j) ,u(i,j), i=1,N+1)    !((u(i,j) , i=1,N+1), J=1,M+1)
              WRITE(10,*)
              !WRITE(10,FMT='(2F20.5)') (x(i), u(i,2), i=1,N)        !((u(i,j) , i=1,N+1), J=1,M+1)
              WRITE(6,'(50("-"))') 
           END DO 
            END IF

           RETURN   
         END SUBROUTINE 


!-----------------------------------------------------------------------

      END MODULE

and the drive main program ..

  PROGRAM main 
       USE BURGER_2
       IMPLICIT NONE 

       REAL(DP) , DIMENSION (N+1) :: xx
       REAL(DP) , DIMENSION (M+1) :: tt
       REAL(DP) , DIMENSION (n+1,M+1) :: UU
      
       CALL burger_EXPLICIT(xx,tt,UU)

        
       STOP 
      END

I have a questions ..
1) I don't know why but if the domain is smaller (ex. L=2) che program give a strange result !

2) one other thing is i've used for intialize the matrix U a sinusoidal wave (take from an example found in internet !) could somebody explain which several condition I can use excluding the condition used here ..

3) i see on the wiky https://www.cfd-online.com/Wiki/Burgers_equation the solution based on Finite volumes method ! i really don't understand 2 things : what is X_c ? and why the explicit solution is only space based ? and for the time ?

Thanks in advance
Marco

[FMDenaro]

What do you mean for "strange results"? Please add a plot.
Then I see this instruction that has nothing to do with the CFL condition.

CFL = DT/DX**2

In the Wiki page the term explicit is used for the explicit formula of the discrete spatial derivatives. Implicit is used as counterpart of the formulas for the compact (and implicit) formulas. In this framework, it has nothing to do with the explicit/implicit time integration.

Then I suggest to follow some examples of the books:
http://mathcenter.hust.edu.cn/Upload...98740d59f8.pdf

http://www.cambridge.org/it/academic...I9Radx3VqTX.97

[drudox]

Originally Posted by FMDenaro

What do you mean for "strange results"? Please add a plot.
Then I see this instruction that has nothing to do with the CFL condition.

CFL = DT/DX**2

In the Wiki page the term explicit is used for the explicit formula of the discrete spatial derivatives. Implicit is used as counterpart of the formulas for the compact (and implicit) formulas. In this framework, it has nothing to do with the explicit/implicit time integration.

Then I suggest to follow some examples of the books:
http://mathcenter.hust.edu.cn/Upload...98740d59f8.pdf

http://www.cambridge.org/it/academic...I9Radx3VqTX.97

Sorry .. CFL = DT/DX

[FMDenaro]

Originally Posted by drudox

Sorry .. CFL = DT/DX

you have to correct that considering also the diffusive constraint...however, in general the CFL contains the velocity that changes in time and space, so that you should consider at each time step to check the condition. However, for the Burgers exquation the velocity does not exceed the maximun at the initial condition, so the assignement CFL=DT/DX is valid only if umax(t=0)<=1