2

I have checked all issues regarding to solving nonlinear PDE numerically. I however try to solve following equation via NDSolve function and get some troubles. enter image description here

And this is my code for above-mentioned equations

rw = 0.05;
Sy = 0.15;
Kr = 0.0001*3600;
Q = 0.01;

sys = {Sy*Derivative[0, 1][h][r, t] == 
   Kr*h[r, t]*((Derivative[2, 0][h][r, t] + Derivative[1, 0][h][r, t]/
        r) + (Derivative[1, 0][h][r, t])^2),
  2*Pi*rw*Kr*h[rw, t]*Derivative[1, 0][h][rw, t] == -Q,
  h[100, t] == 0,
  h[r, 0] == 0.00001

  }; sol = 
 NDSolve[sys, {h}, {r, rw, 100}, {t, 0, 100000}, 
  Method -> "MethodOfLines"]

But the value evaluated by the numerical result is equal to it's initial condition and obviously wrong. Do I miss something in the code?

LingLong
  • 329
  • 1
  • 6
  • h[100, t] == 0, h[r, 0] == 0.00001 tries to assign two different values to h[100, 0]. This needs to be fixed. Also, 2*Pi*rw*Kr*h[rw, t]*Derivative[1, 0][h][rw, t] == -Q is an unusual boundary condition, and I am uncertain how NDSolve will respond to it. – bbgodfrey Aug 10 '17 at 23:45
  • 2
    To be more specific, adding Method -> {"MethodOfLines", "DifferentiateBoundaryConditions" -> {True, "ScaleFactor" -> 100}} to NDSolve will fix your code. (You'll probably need PlotRange->All in Plot3D, too. ) – xzczd Sep 16 '17 at 14:34
  • I do not think that this question is a duplicate of the linked question (and especially not the answers contained there in) – user21 Jul 06 '18 at 07:23
  • 1
    @user21 Would you be willing to write an answer? – halirutan Jul 06 '18 at 12:47
  • 1
    @halirutan The comment by xzczd appears to give the correct answer. – bbgodfrey Jul 07 '18 at 21:55
  • @xzczd, do you want to post your comment as an answer? – user21 Jul 09 '18 at 05:31
  • @user21 Well, I can't remember clearly, but I think this post was "successfully" marked as duplicate of this post? If the solution in my comment above is correct, then I think our previous decision is right. How about marking it as duplicate again? – xzczd Jul 09 '18 at 07:17

0 Answers0