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[Garth Wells <question107819@xxxxxxxxxxxxxxxxxxxxx>]

Question #107819 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/107819

    Status: Open => Answered

Garth Wells proposed the following answer:

On 30/04/10 17:58, cutejeff wrote:
> Question #107819 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/107819
>
>      Status: Answered =>  Open
>
> cutejeff is still having a problem:
> Thank you for both of your suggestions.
> Dr. Wells:  you meant the concomitant term from integration by parts might not be zero, but I implicitly set to zero. Do I understand it correctly?
>

Yes.

Garth

>   What I did for the B.C. was that I made the domain big enough and set 0
> for B.C. at both ends. I understand u^3*d2u/dx2 need to be taken
> integration by parts, but according to my BC setting, the concomitant
> term is indeed zero.
>
> Thank you again for your time to read my problem. Let me describe it in
> details.
>
> I want to use this evolution equation to simulate the thin film flow on
> an incline. The PDE is derived using 2D Navier-Stokes equation, coupled
> with continuity equation and kinematic condition at free surface. See
> Acheson's book for detailed derivations.
>
> Acheson, D.J., Elementary Fluid Dynamics. Oxford University Press, 1990.
>
> In this 1D PDE,
>
> du/dt+3*lmbda*u^2*du/dx*(sina-cosa*du/dx)-lmbda*u^3*cosa*d2u/dx2=0
>
> u is the height of the free surface. I use a parabola “cap” as the initial condition
> u=0.3[1-〖(x-2)〗^2] for1<x<3
> u=0 for the other domain
>
> To make the domain wide enough that in a short time period, the flow
> doesn't cross the boundary. I set the domain mesh = Interval(1000,0,16),
> at least in 12 sec, the flow won't touch the boundaries. Hence, u=0 at
> both ends all the time, which is also my BC.
>
> According to the derivations, if I integrate u over the domain, I should
> get the mass of the fluids, it shouldn't change with time due to the
> conservation of mass.  But the fact is that it grows for my Fenics code.
> I couldn't find any problem in my model so far.
>
> I just start to learn the finite element processes, not very good at it.
> But I really have lots interests on this Fenics package. Any helps will
> be appreicated.
>

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