dolfin team mailing list archive

[Alexander Jarosch <alexanj@xxxxx>]

If I use a stabilized first-order form, the oscillations on the boundary 
disappear. I have a curved surface in the fluid and there the pressure 
is not correct. If I set the pressure on the curved surface = 0 than the 
horizontal velocities look okay, but the verticals not.
The form was:
------------------------------------
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 + q*div(u) + delta*dot(grad(q), 
grad(p)))*dx
L = dot(v + mult(delta, grad(q)), f)*dx
------------------------------------

Alex

Anders Logg wrote:

> What happens when you run the same problem with first-order
> stabilized? Same oscillations? What effect does the stabilization
> parameter have?
>
> /Anders
>
>
> On Tue, May 23, 2006 at 11:16:15AM -0500, Robert C. Kirby wrote:
>  
>
> > Andy Terrel was doing some very basic Stokes flow with Taylor Hood  
> > and getting some oscillations around the boundary.  I don't know how  
> > to explain this behavior.
> >
> >
> > On May 23, 2006, at 11:14 AM, Alexander Jarosch wrote:
> >
> >    
> >
> > > I use a direct solver and I have a boundary where the velocities =  
> > > 0 and on that boundary the pressure fluctuates even with a mixed  
> > > Taylor-Hood approch.
> > >
> > > Alex
> > >
> > > Garth N. Wells wrote:
> > >
> > >      
> > >
> > > > On Tue, 2006-05-23 at 14:46 +0000, Alexander Jarosch wrote:
> > > >
> > > >        
> > > >
> > > > > Hi,
> > > > >
> > > > > did anyone play around with the stokes solver on more complex  
> > > > > geometries?
> > > > >          
> > > > The demo in src/demo/pde/convection-diffusion solves the Stokes  
> > > > problem
> > > > around a dolphin using a Taylor-Hood element and the result looks OK.
> > > >
> > > > Garth
> > > >
> > > >
> > > >
> > > >        
> > > >
> > > > > I only seem to get something senseful using a stabalized stokes  
> > > > > like:
> > > > >
> > > > > scalar = FiniteElement("Lagrange", "triangle", 1)
> > > > > vector = FiniteElement("Vector Lagrange", "triangle", 2)
> > > > > 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 + q*div(u) + delta*dot 
> > > > > (grad(q), grad(p)))*dx
> > > > > L = dot(v + mult(delta, grad(q)), f)*dx
> > > > >
> > > > > which is fine, but when I compare the solution to another FEM  
> > > > > package, they do not quite match. Was there already some  
> > > > > benchmarking done?
> > > > >
> > > > > cheers,
> > > > >
> > > > > Alex
> > > > >
> > > > >          
> > > >
> > > > _______________________________________________
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> > > >
> > > >
> > > >        
> > >      
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> >    
>
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--
Alexander H. Jarosch

Jarðvísindastofnun Háskólans
Institute of Earth Sciences, University of Iceland
Náttúrufræðahús, Askja
Building of Natural Sciences, Askja
Sturlugata 7
IS - 101 Reykjavík
Iceland

Tel.: +354 525 4906
http://raunvis.hi.is/~jarosch/