- #1
nickthequick
- 53
- 0
Hi,
I've been trying to solve
[itex]\frac{\partial \vec{u}(x,y,z,t)}{\partial t} = \nu \nabla^2 \vec{u}(x,y,z,t)[/itex]
Where the Laplacian is 3-d. My initial conditions are
[itex]\vec{u}(x,y,z,0)=\vec{u_o}(x,y,z)[/itex].
And my BC is that
[itex](u_z,v_z,w)= 0 [/itex] at z=0. where [itex]\vec{u} = (u,v,w)[/itex]
I want to solve for [itex]\vec{u}(x,y,0,t)[/itex] i.e. at z=0.
Here, [itex] (x,y) \in \mathbb{R}, z \in (-\infty,0), t\in \mathbb{R}^+ [/itex].
Is there an analytic way to do this? So far I have only come across numerical schemes or examples for lower dimensions.
Any suggestions would be appreciated,
Nick
Nick
I've been trying to solve
[itex]\frac{\partial \vec{u}(x,y,z,t)}{\partial t} = \nu \nabla^2 \vec{u}(x,y,z,t)[/itex]
Where the Laplacian is 3-d. My initial conditions are
[itex]\vec{u}(x,y,z,0)=\vec{u_o}(x,y,z)[/itex].
And my BC is that
[itex](u_z,v_z,w)= 0 [/itex] at z=0. where [itex]\vec{u} = (u,v,w)[/itex]
I want to solve for [itex]\vec{u}(x,y,0,t)[/itex] i.e. at z=0.
Here, [itex] (x,y) \in \mathbb{R}, z \in (-\infty,0), t\in \mathbb{R}^+ [/itex].
Is there an analytic way to do this? So far I have only come across numerical schemes or examples for lower dimensions.
Any suggestions would be appreciated,
Nick
Nick