Arithmetic overflow in Fortran 95

  1. 1. The problem statement, all variables and given/known data

    Wrote a code using Fortran 95 to solve for an advection-dispersion equation but at the spatial steps specified at dx = 20 m over a total length, L of 20000 m, I keep getting an arithmetic overflow error.

    I have run this same program at smaller spatial intervals (dx = 200 m and dx = 2000 m) and they worked perfectly. There must be something about the total number of iterations that Fortran is trying to perform that makes it incapable of computing it (I'm not actually sure).

    I'm a novice at using Fortran but curious if this has anything to do with the size of the concentration values that are being computed being too small (i.e. smaller than 10^-38). Does this have anything to do with double precision?

    2. Relevant equations

    The scheme used to solve the numerical solution to the ADE is an finite differenece upwind scheme.

    The first equation in the code under the two "do" statements defines this upwind scheme within the internal bounds of the system.

    The second equation in the code outside of the two "do" statements defines the boundary condition at X = L.

    3. The attempt at a solution

    module global ! Module is used to define arrays and use in main program blocks

    implicit none
    real len, dx, k, Dl
    real, allocatable, dimension (:, :) :: conc ! I used allocatable arrays so that the size of
    ! the array can be changed, not necessary for this
    ! simple of a problem
    real, allocatable, dimension (:) :: tim
    integer ndx, i, n

    end module global

    program main
    use global

    real dt , tottime, u

    This is where you write out what you're going to be doing. You can just link to where a
    ! source file is located, but make sure you do it.

    dt = 30. ! unit is seconds
    len = 20020. ! unit is meters
    tottime = 44000. ! unit is seconds (43200 seconds in half a day)
    ndx = 1001 ! number of grid points - we want 10 cells so we start at 1.
    u = 0.25 ! unit is m/s
    Dl = 50. ! unit is m^2/sec
    k = 0.1 / 86400. ! unit is sec^-1
    nts = (tottime) / dt ! number of time steps
    dx = len / real(ndx) ! grid spacing

    ! Allocate the arrays, conc(entration), and tim(e).
    allocate (conc ( ndx , nts ), tim ( nts ))

    conc = 0.0 ! set initial concentration elements to 0 mg/L
    tim = 0.0 ! initial time is zero
    conc (1, :) = 100. ! set BC on LHS to 100 mg/l for all time

    ! Run the internal finite difference equation and populate the array conc ()

    do n = 1, nts - 1
    tim (n) = dt * (n - 1)
    do i = 2, ndx - 1
    conc (i, n + 1) = conc (i, n) - u * (dt / dx) * (conc (i, n) - conc (i - 1, n)) &

    + Dl * (dt / (dx**2)) * (conc (i + 1, n) - 2 * conc (i, n) + conc (i - 1, n)) - k * dt * conc (i, n)
    end do
    conc (ndx, n + 1) = conc (ndx, n) - u * (dt / dx) * (conc (ndx, n) - conc (ndx - 1, n)) &
    + Dl * (dt / dx**2) * (2 * conc (ndx - 1, n) - 2 * conc (ndx, n)) - k * dt * conc (ndx, n)
    end do

    ! Set BC on RHS where c (ndx + 1, nts) = c (ndx - 1, nts)
    ! Write the array to a file

    open (10, file = 'C:\g95\fortran\CEE 573\Problem Set 5\upwind20.csv', status = 'unknown')

    ! Write the column headings
    write (10, 100) (tim (n) / 86400., n = 1, nts, 10)
    100 format ('X, ',2x, 10000 ('t=', f8.4, ','))

    ! Write the columns
    do i = 1, ndx
    x = dx * (i - 1)
    write (10, 110) x, (conc (i, n), n = 1, nts, 10)
    110 format (f10.1, ',', 10000 (f8.4, ','))
    end do

    end program main
     
  2. jcsd
  3. jedishrfu

    Staff: Mentor

    does the computer say what line is getting the overflow error?
     
  4. Yeah, it said the error was on line 47 which is the second line of this equation (internal finite difference equation):

    conc (i, n + 1) = conc (i, n) - u * (dt / dx) * (conc (i, n) - conc (i - 1, n)) &
    + Dl * (dt / (dx**2)) * (conc (i + 1, n) - 2 * conc (i, n) + conc (i - 1, n)) - k * dt * conc (i, n)
     
  5. Mark44

    Staff: Mentor

    To debug this, break up the expression on the right side, so that you do the computation in at least three assignment statements. That should help you determine which term is causing problems.
     
  6. Okay, I did that. And so I put the k term on line 48 and the error occurs on line 48. So it must be something with the k term. Why would it not do this if I set the spatial steps higher at dx = 200 m and dx = 2000 m instead of dx = 20 m?
     
  7. jedishrfu

    Staff: Mentor

    so now you print out the value of k, dt,i,n and conc(i,n) separately
    and see which var is causing the issue.
     
    Last edited: Feb 29, 2012
  8. If you have downstream boundary conditions instabilites may exist unless the Peclet number is kept small by making the spatial discritization small. The grid spacing must be sufficiently small so the Laplacian dominates the equation. This can be accomplished by grid refinement. For additional information google 'grid peclet number'.
     
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