[Users] Thorn Periodic

[Erik Schnetter]

Hassan

Thorn RotatingSymmetry90 assumes Cartesian coordinates; it will not
help you. Thorn Periodic is the right thorn to use, with one periodic
direction, e.g. y, just as you did.

What exactly is going wrong? One has to be careful with the number of
grid points, number of boundary points, and whether the boundary is on
or in between grid points. Here is my first attempt:

I assume you use 3 ghost zones, that you want to have a grid point at
phi=-pi (and at phi=+pi), and that you want to have a grid spacing of
2pi/36 in the phi direction:

# How we want to specify things
CoordBase::domainsize = "minmax"
CoordBase::spacing = "numcells"

# This is the easy part
CoordBase::ymin = -3.14...
CoordBase::ymax = +3.14...
CoordBase::ncells_y = 36
# Similarly for x and z

# Now the meticulous grid point counting
CoordBase::boundary_size_y_lower = 3   # 3 boundary points, since
there are 3 ghost points
CoordBase::boundary_size_y_upper = 3
CoordBase::boundary_shiftout_y_lower = 1

The last line is probably difficult to guess. It means that the point
at the lower boundary (at y=-pi) is not a boundary point; the boundary
begins only one gridpoint below. This means that this gridpoint is
evolved in time. Conversely, the point at y=+pi is a boundary point;
it is not evolved in time, since it is set via the periodicity
condition. This means that the points y=-pi and y=+pi are treated
differently – this may be confusing at first, but is actually correct,
since your domain is in this case [-pi; +pi), i.e. the lower boundary
is included while the upper boundary is not.

The thorn CoordBase has some documentation with figures that explain
these parameters.

Note that the number of cell in the phi direction needs to be even if
you want a grid point at phi=0.

-erik

On Tue, Mar 1, 2011 at 3:47 PM, Seyyed Mohammad Hassan Halataei
<smhhalataei at gmail.com> wrote:
> Dear Erik,
>
> Thank you for your respond. I want to use cylindrical coordinates in my
> problem (r, phi, z) and I think I need a physical boundary condition for phi
> ,rather than a symmetry. It seems rotational boundary condition can be
> helpful and I thought if I use periodic boundary condition for phi (namely ,
> periodic_y = yes) the code should satisfy my demand . However, it could not.
>
> Am I on the right track ?
> I think RotatingSymmetry90 cannot do that , because I want to have the full
> range [-PI, PI] and evolve it . All I need is connecting two ends of the
> grid in phi direction (or y) together . In other words, I like to tape -PI
> to PI.
>
> Do you think the thorn Periodic is the appropriate thorn or there is a
> better thorn which can do that for me ?
>
> Thank you
> Hassan
>
>
> On Mon, Feb 28, 2011 at 5:37 PM, Erik Schnetter <schnetter at cct.lsu.edu>
> wrote:
>>
>> Hassan
>>
>> The current version of this thorn is located in an svn repository at
>> <http://svn.cactuscode.org/arrangements/CactusNumerical/Periodic>.
>> However, this thorn implements a toroidal symmetry, not a rotational
>> symmetry. Can you describe the symmetry that you are trying to apply?
>> For example, there is another thorn CactusNumerical/RotatingSymmetry90
>> that may be more suitable. There is also another thorn available that
>> implements a Cartoon symmetry.
>>
>> We describe much of our code at <http://einsteintoolkit.org>, and we
>> use the mailing list <users at einsteintoolkit.org> for discussion. Would
>> you mind using this mailing list instead of keeping this conversation
>> private? The mailing list has the advantage that others will also be
>> able to help when I don't know the answer.
>>
>> -erik
>>
>> On Mon, Feb 28, 2011 at 6:20 PM,  <halatae1 at illinois.edu> wrote:
>> > Dear Dr. Schnetter,
>> >
>> > I am Hassan Halataei, working in Professor Shapiro's Numerical
>> > Relativity group in Univ. of Illinois at Urbana-Champaign. I am trying to
>> > use the thorn Periodic you have written in 2003 to implement rotational
>> > symmetry in my problem (Single Black hole surrounded by an accretion disk) .
>> > I read the 2-page documentary of the thorn and acted according to that .
>> > However, the  thorn does not work for me . I tried several different things
>> > for days to make it work , however the result does not obey periodic
>> > boundary condition . I was wondering if you let me know if there is anything
>> > that I missed or any other consideration that I must take care of ?
>> >
>> >
>> > Thank you
>> > Hassan
>> >
>>
>>
>>
>> --
>> Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/
>
>



-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/