dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, May 30, 2006 at 10:07:47AM +0000, Alexander Jarosch wrote:
> Hi everybody.
> 
> There was a short discussion about Stokes flow on complex geometries. I 
> would like to report that a ffc form like the one below works well on 
> complex geometries, I still only have a factor of 1.2 offset in 
> magnitude if I compare it with another fem model.  I would like to get 
> some feedback about this form, whether it is okay or not from the 
> developers point of view.
> 
> much appreciated,
> 
> Alex
> 
> ffc form -------------------
> 
> scalar = FiniteElement("Lagrange", "triangle", 1)
> vector = FiniteElement("Vector Lagrange", "triangle", 1)
> system = vector + scalar
> 
> (v, q) = TestFunctions(system)
> (u, p) = TrialFunctions(system)
> 
> f = Function(vector)
> h = Function(scalar)
> nu = Function(scalar)
> 
> beta  = 0.2
> delta = beta*h*h
> 
> a = (nu*dot(grad(v), grad(u)) - div(v)*p + nu*q*div(u) + 
> delta*dot(grad(q), grad(p)))*dx
> L = dot(v + mult(delta, grad(q)), f)*dx

I think it looks a little strange. The difference from what you had
before seems to be that you have included the viscosity in the
incompressibility term:

    nu*q*div(u)

Is this what makes the difference? If so, I don't know why this
helps. It's certainly ok to put it there since you're solving for
div(u) = 0 anyway, so nu*div(u) = 0 is also correct.

In some way, it corresponds to a smaller penalty for compressibility
when the viscosity is small which might be reasonable.

/Anders