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Math Help - Solving a streamline function PDE

  1. #1
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    Solving a streamline function PDE

    Hi,

    I am trying to solve an streamline function. I have found this PDE for the steamline function, \psi .

    \frac{\partial}{\partial  z}\left(f\frac{\partial \psi }{\partial  z} \right)+  \frac{\partial}{\partial  x}\left(a.f\frac{\partial \psi }{\partial  x} \right)-\frac{\partial F}{\partial  z}=0

    with the boundary conditions of:

    \frac{\partial \psi }{\partial  x}=0 at z=0

    \frac{\partial \psi }{\partial  x}=0 at z=h

    \frac{\partial \psi }{\partial  z}=b at x=0

    \frac{\partial \psi }{\partial  z}=b at x=\infty

    where a, b and h are constants. f and F are functions of (x,z). Does anybody know if this PDE can be solved? Thanks.
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  2. #2
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    Do you know the forms of f and F?
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  3. #3
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    No, the problem is that the functions f and F are actually functions of another variable say Sw which is a function of x and z

    F=F(S_w)=F(S_w(x,z))=F(x,z)
    f=f(S_w)=f(S_w(x,z))=f(x,z)

    The ultimate goal is to find S_w but I need to solve this equation in this general form if possible, then I use the results in another equation to solve for S_w. Please let me know if it is not possible to solve it like this so I try to find another method to solve S_w. Thanks.
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  4. #4
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    I don't think that I can solve it but if you post the original problem there might be another approach.
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