dolfin team mailing list archive

[cutejeff <question107819@xxxxxxxxxxxxxxxxxxxxx>]

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?

 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.

-- 
You received this question notification because you are a member of
DOLFIN Team, which is an answer contact for DOLFIN.