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Explicit solution of heat/diffusion equation

  1. Nov 23, 2007 #1
    I am trying to use a explicit FDM for transient 1d conditions with linear elements for specific diffusion equation:

    ds/dt=D(x)*d2s/dx2+R(s)

    the problem is that I am using different, nonlinear functions describing diffusion constant D(x) and reaction rate R(s).
    The diffusion parameter is dependent on position along x and in general case is a function with non-continuous dD(x)/dx at some points. I am using average value of diffusion parameter for each linear element but the solution seems to be not right. I think that is the problem, because when I use constant D everything looks all right. Especially plot of d2s/dx2 is very wired.
    What I am doing wrong?
    Thanks.
     
  2. jcsd
  3. Nov 23, 2007 #2

    Chris Hillman

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    Science Advisor

    Huh?

    FDM?

    Wired as in wire-frame plot? Or is that "weird"?
     
  4. Nov 23, 2007 #3
    'wired' as strange. it has to many bumps. should be less compicated in places where D is changing
     
  5. Nov 28, 2007 #4

    Chris Hillman

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    Science Advisor

    Gentle hint

    So, weird as in "strange"? Too many bumps? Less complicated? And what is FDM? "Finite difference method", perchance? Is your diffusion equation
    [tex]
    \frac{\partial u}{\partial t} = f(x) \, \frac{\partial^2 u}{\partial x^2}+ g(u)
    [/tex]
    where u is an unknown function of x,t and f,g are known functions of one variable, and where f is continuous but only piecewise differentiable? You hinted at initial conditions--- what are they?
     
    Last edited: Nov 28, 2007
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