Dear Sir,
So far I have used step-17 and step -18 to apply body force and zero
Dirichlet b.c.'s. I have attached the result below:-).
I am now trying to implement Neumann b.c.'s on inner wall.
So this is what i am thinking:
#Create a template such that it returns a vector with constant magnitude
and direction indicated by unit vector along radial direction. Does it make
sense?
Thanking you.
Himal.
On Thu, 17 Nov 2022, 10:44 am HIMAL MAGAR, <075bme018.hi...@pcampus.edu.np>
wrote:
> Dear Sir,
> The equation is Poisson's equation with mixed boundary conditions. The
> domain is a cylinder shell. I am trying to apply Homogeneous Boundary
> Condition on the bottom face as done in step-18 and Neumann Boundary
> Condition on the inner surface of the cylinder. I have already derived a
> weak formulation of the equation and come up with the term you have
> mentioned. When applying in the code, do I have to construct a separate
> template for "pressure"? or can i just put the value explicitly in the
> cell_rhs component for Neumann boundary? And if I do the latter, what will
> be the direction of the pressure relative to the face?
>
> Thank you.
> Himal
>
> On Thu, Nov 17, 2022 at 10:03 AM Wolfgang Bangerth <bange...@colostate.edu>
> wrote:
>
>> On 11/16/22 03:58, HIMAL MAGAR wrote:
>> > I am trying to apply Neumann boundary condition(pressure) on inner wall
>> of a
>> > cylinder. So far, I have followed Lecture 21.55 to apply this condition
>> in 2d
>> > (in step-6 and step-8) and succeeded. But when it came to 3d case, I am
>> having
>> > hard time understanding how to implement pressure which is always
>> normal to
>> > the faces of inner wall.
>>
>> Himal:
>> the first step in these cases is always to write down the weak
>> formulation of
>> the equation. Can you explain what the equation is and where Neumann
>> boundary
>> conditions enter? There shouldn't really be a difference between 2d and
>> 3d,
>> you will generally just end up with a term of the form
>> (p, n.phi)_{Gamma_N}
>> where p is the prescribed pressure, n the normal vector, and phi a
>> (vector-valued) test function, all integrated over that part of the
>> boundary
>> Gamma_N where you impose Neumann boundary conditions. The form of this
>> integral does not depend on whether you are in 2d or 3d.
>>
>> Best
>> W>
>>
>> --
>> ------------------------------------------------------------------------
>> Wolfgang Bangerth email: bange...@colostate.edu
>> www: http://www.math.colostate.edu/~bangerth/
>>
>>
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