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Laplace equation with boundary condition

  1. Jul 31, 2012 #1
    Good afternoon,

    I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that:

    2[itex]\phi[/itex]=0
    [itex]\phi[/itex]x=1 when x=-A and x=A
    [itex]\phi[/itex]y=0 when y=-B and y=B
    [itex]\phi[/itex]z=0 when z=Ztop and z=Zbot


    I have tried different solutions that look like
    [itex]\phi[/itex]=x+Ʃ(cos(α(x+A))cos(β(y+B))cosh(γ(z-Ztop))

    α=n*PI/A n=1...∞
    β=m*PI/B m=1...∞
    and α222

    I can't find a solution that satisfy everything.
    I either satisfy the boundary conditions or Laplace equation but not both.
    The problem comes from the need to have a sinh(z)=0 for 2 values...
    I can't figure out how to go around the problem.

    Any advice would be really nice.

    Thanks
    Anne

    PS: I have the three permutation to find [itex]\phi[/itex]x=1 then [itex]\phi[/itex]y=1 and [itex]\phi[/itex]z=1
    I have the same problem in the three cases.
     
  2. jcsd
  3. Aug 11, 2012 #2
    Try x+c as the solution
     
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