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MathGroup Archive 2007

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Re: Convective diffusion equation in 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79857] Re: Convective diffusion equation in 2D
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Tue, 7 Aug 2007 01:27:44 -0400 (EDT)
  • References: <f8v09f$cbk$1@smc.vnet.net><f91i6t$5hi$1@smc.vnet.net> <f943hn$m56$1@smc.vnet.net>
  • Reply-to: "Dr. Wolfgang Hintze" <weh at snafu.de>

Sorry for interfering,
but I had a similar question before.

Using the procedure of Jens in the form

s = First[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}]]]

{u[x, y, t] -> InterpolatingFunction[][x, y, t]}

extractiing the solution into a function h

h[x_, y_, t_] = u[x, y, t] /. s

InterpolatingFunction[][x, y, t]

and finally plotting the result using

t = 1;
Plot3D[h[x, y, t], {x, -1, 1}, {y, -1, 1}]

or the sequence

For[t = 1, t <= 2, t = t + 0.1, Plot3D[h[x, y, t],
{x, -1, 1}, {y, -1, 1}, PlotRange -> {0, 0.45}]]

looks very nice.

Best regards,
Wolfgang


"dantimatter" <dantimatter at gmail.com> schrieb im Newsbeitrag 
news:f943hn$m56$1 at 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}
>>     ]
>>   ]
>>
>> may do that .. Ignore the warnings you get with the
>> statement above, the reason are the initial conditions
>> and you may have other.
>
> Hi Jens,
>
> I wasn't able to plot the result.  Have you tried this and
> successfully plotted it?
>
> Cheers,
> Dan
>
> 



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