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 > >