Using PETSc in structured c-grid for CFD and multigrid

[Berend van Wachem]

Hi Ben,

It will probably work, but it will be more expensive. If you use an 
implicit algorithm to solve the flow, it really pays off to have the 
boundary conditions implicit as well. Explicit boundary conditions 
mean you will need additional iterations, which is really unnecessary 
in your case. Why not put the dependency directly in the matrix?

Berend.


> Hi,
>
> somone suggested that I treat that face as a dirichlet boundary
> condition. after 1 or a few iterations, the face value will be
> updated and it will be repeated until covergerence. I wonder if that
> is possible as well?
>
> It'll make the job much easier, although the iteration may take
> longer...
>
> On 2/1/07, Barry Smith <bsmith at mcs.anl.gov> wrote:
> > The glueing might be able to be handled by using periodic for that
> > dimension of the DA you create. But this gets tricky if you have
> > any nodes that have "an extra degree of freedom".
> >
> >   Barry
> >
> > On Wed, 31 Jan 2007, Berend van Wachem wrote:
> > > Hi Ben,
> > >
> > > The challenge in your problem is how you "glue" the C grid in
> > > the back; there you will need to do some additional scattering.
> > > I would set-up the IS for this, and then use that to scatter the
> > > values into "ghostcells" which will be present on the block(s).
> > >
> > > Berend.
> > >
> > > > Thank you Berend! I'll go through DA again. I'm also looking
> > > > at HYPRE. Its way of creating grids and linking them seems
> > > > intuitive. Btw, is there a mailing list for HYPRE similar to
> > > > PETSc to discuss problems? I find that their explanation are
> > > > quite brief.
> > > >
> > > > I tried to install HYPRE 2.0 on windows using cygwin but it
> > > > failed. I then install it as an external software thru PETSc.
> > > > I think it's installing HYPRE 1.0 or something. But similarly,
> > > > there's illegal operation.
> > > >
> > > > Installing HYPRE 2.0 on my school's linux worked, though
> > > > there's seems to be some minor error. So what's the best way
> > > > to employ multigird? Is it to install as an external software
> > > > thru PETSc or just use HYPRE on its own?
> > > >
> > > > Btw, it will be great if you can send me parts of your code
> > > > regarding DA.
> > > >
> > > > Thank you very much!
> > > >
> > > > On 1/26/07, Berend van Wachem <berend at tfd.chalmers.se> wrote:
> > > > > Hi,
> > > > >
> > > > > I am not an expert - but have used PETSc for both structured
> > > > > and unstructured grids.
> > > > >
> > > > > When you use an unstructured code for a structured grid,
> > > > > there is additional overhead (addressing, connectivity)
> > > > > which is redundant; this information is not required for
> > > > > solving on a structured grid. I would say this is maximum a
> > > > > 10% efficiency loss for bigger problems - it does not affect
> > > > > solving the matrix, only in gathering your coefficients. I
> > > > > would not rewrite my CFD code for this.
> > > > >
> > > > > If you only deal with structured grids, using the PETSc DA
> > > > > framework should work for you - you are not saving all
> > > > > connectivity. The DA framework is not difficult at all,
> > > > > according to my opinion. Look at a few examples that come
> > > > > with PETSc. I use a block structured solver - using multiple
> > > > > DA's within one problem. Let me know if you are interested
> > > > > in this, and I can send you parts of code.
> > > > >
> > > > > Multigrid is certainly possible (I would reccomend through
> > > > > HYPRE, discussed on the mailinglist, although I still have
> > > > > problems with it), but the question is how efficient it will
> > > > > be for your CFD problem. For an efficient multigrid in CFD,
> > > > > it is important to consider the coefficient structure
> > > > > arising from the momentum equations - the grouping of cells
> > > > > should occur following the advection term. Only then will
> > > > > you achieve linear scaling with the problem size. For
> > > > > instance, consider a rotating flow in a square box. Most
> > > > > multigrid algorithms will group cells in "squares" which
> > > > > will not lead to a significant improvement, as the flow
> > > > > (advection, pressure grad) does not move in these squares.
> > > > > In fact, to have an efficient multigrid algorithm, the cels
> > > > > should be grouped along the circular flow. As this cannot be
> > > > > seen directly from the pressure coefficients, I doubt any
> > > > > "automatic" multigrid algorithm (in Hypre or Petsc) would be
> > > > > able to capture this, but don't quote me on it - I am not
> > > > > 100% sure. So concluding, if you want to do efficient
> > > > > multigridding for CFD, you will need to point out which
> > > > > cells are grouped into which structure, based upon the
> > > > > upwind advection coefficients.
> > > > >
> > > > > Good luck,
> > > > >
> > > > > Berend.
> > > > >
> > > > > > Hi,
> > > > > >
> > > > > > I was discussing with another user in another forum
> > > > > > (cfd-online.com)
> > > > >
> > > > > about
> > > > >
> > > > > > using PETSc in my cfd code. I am now using KSP to solve my
> > > > > > momentum and poisson eqn by inserting values into the
> > > > > > matrix. I was told that using PETSc
> > > > > > this way is only for unstructured grids. It is very
> > > > > > inefficient and much slower if I'm using it for my
> > > > > > structured grid because I am not
> > > > >
> > > > > exploiting
> > > > >
> > > > > > the regular structure of my grid.
> > > > > >
> > > > > > Is that true? I'm solving flow around airfoil using
> > > > > > c-grid.
> > > > > >
> > > > > > So how can I improve? Is it by using DA? I took a glance
> > > > > > and it seems quite
> > > > > > complicated.
> > > > > >
> > > > > > Also, is multigrid available in PETSc? Chapter 7 discusses
> > > > > > about it but
> > > > >
> > > > > it
> > > > >
> > > > > > seems very brief. Is there a more elaborate tutorial
> > > > > > besides that c examples?
> > > > > >
> > > > > > Hope someone can give me some ideas.
> > > > > >
> > > > > > Thank you.