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MathGroup Archive 2007

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Re: Convective diffusion equation in 2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79770] Re: Convective diffusion equation in 2D
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 4 Aug 2007 05:49:07 -0400 (EDT)
  • References: <f8v09f$cbk$1@smc.vnet.net>

Hi,

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.

Regards
   Jens

dantimatter wrote:
> Hello all,
> 
> I'm trying to find a nice and neat way to numerically solve the
> convective diffusion equation
> 
> da/dt = D (d^2/dx^2 + d^2/dy^2) a - v da/dx
> 
> where a is the concentration of my solute, D is the diffusion
> constant, and v is the surrounding fluid velocity in the x direction.
> I thought that there was a small chance that maybe someone else here
> has attempted something similar.
> Is it even possible to solve this equation? As always, any suggestions
> would be much appreciated.
> 
> Cheers,
> Dan
> 
> 


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