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[ff3d-users] Stationary Navier-Stokes equations / Flow past cylinder pro
From: |
Dominique Deloison |
Subject: |
[ff3d-users] Stationary Navier-Stokes equations / Flow past cylinder problem |
Date: |
Fri, 18 May 2007 21:50:01 +0200 |
User-agent: |
Mozilla Thunderbird 1.0.6 (Windows/20050716) |
Hi,
I try to solve the classical problem of the flow past a cylinder at low
Reynolds number. This is not the actual problem I am interested in but a
good starting point.
I can make two simplifications:
- remove the temporal part (stationary problem),
- suppose the fluid is imcompressive.
The equations are then:
rho*(u*du/dx+v*du/dy+w*du/dz)=-dp/dx+mu*(d2u/dx2+d2u/dy2+d2u/dz2)
rho*(u*dv/dx+v*dv/dy+w*dv/dz)=-dp/dy+mu*(d2v/dx2+d2v/dy2+d2v/dz2)
rho*(u*dw/dx+v*dw/dy+w*dw/dz)=-dp/dz+mu*(d2w/dx2+d2w/dy2+d2w/dz2)
du/dx+dv/dy+dw/dz=0
u,v,w are zero on the cylinder surface. There is a global flow motion
(in x direction).
The convective part is non linear. So I suppose it is necessary to solve
this iteratively.
I tried to use the Navier-stokes example but I had problems because it
is outdated. I tried to rewrite it using the new way to write the
"convect" keyword but failed.
I then attempted to write a variational form but I have to say I am not
very good at this.
Could somebody give me a hand ?
Many thanks.
- [ff3d-users] Stationary Navier-Stokes equations / Flow past cylinder problem,
Dominique Deloison <=