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MathGroup Archive 2007

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Re: Convective diffusion equation in 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79817] Re: Convective diffusion equation in 2D
  • From: dantimatter <dantimatter at gmail.com>
  • Date: Sun, 5 Aug 2007 04:56:54 -0400 (EDT)
  • References: <f8v09f$cbk$1@smc.vnet.net><f91i6t$5hi$1@smc.vnet.net>

> With[{\[ScriptCapitalD] = 1/8, v = 1/4},
>   sol = NDSolve[{
>      D[u[x, y, t],
>        t] == \[ScriptCapitalD] (D[u[x, y, t], {x, 2}] +
>           D[u[x, y, t], {y, 2}]) - v*D[u[x, y, t], x],
>      u[-1, y, t] == 0, u[1, y, t] == 0,
>      u[x, -1, t] == 0, u[x, 1, t] == 0,
>      u[x, y, 0] == Piecewise[{{1, Sqrt[x^2 + y^2] <= 0.5}}, 0]},
>     u[x, y, t], {x, -1, 1}, {y, -1, 1}, {t, 0, 2}
>     ]
>   ]

ok, so i got the above to work when i ran it on a more powerful
machine. thanks for the advice.  the problem i'm having now is in
defining the boundary conditions.  what i'd like is to have a circular
'source' at which the concentration is always constant, but i don't
know about any of the other boundaries.  i guess i could say that the
concentration is zero at infinity.  any advice on how to implement
these boundary conditions??

many thanks,
dan



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