Mixed Function Space: I Know One, I Want the Other

On 29 May 2012 23:31, Stav Gold <email address hidden> wrote:
> New question #198825 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/198825
>
> I have, through nefarious means, obtained the pressure of a particular system. Now, I want to know the velocity of that system by relating the two through a variational form and solving over a mixed function space.
>

If you already know the pressure, why do you need a mixed element?
Could you just feed the pressure in as a Function?

Garth

> I know that assigning the pressure function to a shallow copy of the scalar component of a function on the mixed space is the first step, but solving this system produces NaN's in the velocity field. Minimal code follows--anyone have an idea what's going on?
>
> Space = FunctionSpace(mesh, "CG", 2)
> VSpace = VectorFunctionSpace(mesh, "CG", 2)
> W = VSpace*Space
>
> v = TestFunction(Space)
> P = TrialFunction(Space)
>
> (r,q)      = TestFunctions(W)
> (u,Pv)     = TrialFunctions(W)
> PNext = Function(Space)
> PhiNext = TrialFunction(Space)
> Phi = Function(Space)
> Phi.interpolate(Phi_init)
>
> pLeft = -inner(grad(P),grad(v))*(Phi**n)*dx-h2*(Phi**m)*P*v*dx
> pRight = Dx(Phi**n,1)*v*dx
>
> P = Function(Space)
>
> # Phi time-dependence problem set-up
> a = PhiNext*v*dx
> L = (Phi+dt*P*h2*Phi**m)*v*dx
> A = assemble(a)
>
> vv = div(u)*q*dx-Pv*q*dx
> f = Constant(0.0)
> vRight = f*q*dx
> bigu= Function(W)
>
> while t <= T:
>                # Phi, Pressure step
>                pl = assemble(pLeft)
>                pr = assemble(pRight)
>                solver.solve(pl,P.vector(),pr)
>                b = assemble(L)
>                solver.solve(A,PhiNext.vector(),b)
>                Phi.assign(PhiNext)
>
>                # Velocity step
>                VL = assemble(vv)
>                VR = assemble(vRight)
>                uv, us = bigu.split(deepcopy=False)
>                us.assign(P)
>                solve(VL,bigu.vector(),VR)
>
>
>
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> If you already know the pressure, why do you need a mixed element?
> Could you just feed the pressure in as a Function?

Can I do that without using a mixed function space? The pressure is defined on a scalar function space, and the velocity (which I'm wanting to solve for) is defined on a vector function space...

On 25 June 2012 17:45, Stav Gold <email address hidden> wrote:
> Question #198825 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/198825
>
>    Status: Answered => Open
>
> Stav Gold is still having a problem:
>> If you already know the pressure, why do you need a mixed element?
>> Could you just feed the pressure in as a Function?
>
> Can I do that without using a mixed function space? The pressure is
> defined on a scalar function space, and the velocity (which I'm wanting
> to solve for) is defined on a vector function space...
>

Yes. You need to make sure that the integrands in your form are scalars.

Garth

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