[petsc-users] examples of DMPlex*FVM methods

[Jed Brown]

Ingo Gaertner <ingogaertner.tus at gmail.com> writes:

> Hi Matt,
> I don't care if FV is suboptimal to solve the Poisson equation. I only want
> to better understand the method by getting my hands dirty, and also
> implement the general transport equation later. We were told that FVM is
> far more efficient for the transport equation than FEM, and this is why
> most CFD codes would use FVM. Do you contradict? Do you have benchmarks
> that show bad performance for the (parabolic) transport equation

What is the "parabolic transport equation"?  Advection-dominated
diffusion?  The hyperbolic part is usually the hard part.  FEM can solve
these problems, but FV is a good method, particularly if you want local
conservation and monotonicity.

> solved by FVM, or why do you think that FVM was designed only for
> hyperbolic problems?  The decision whether to focus on FEM or FVM is
> quite interesting for me, because it seems like a matter of taste, and
> our professor of numerical methods for CFD seems to strongly prefer
> FVM without a solid basis to justify his preference.
>
> Thanks
> Ingo
>
>
> 2017-04-05 18:56 GMT+02:00 Matthew Knepley <knepley at gmail.com>:
>
>> On Wed, Apr 5, 2017 at 11:50 AM, Ingo Gaertner <ingogaertner.tus at gmail.com
>> > wrote:
>>
>>> Hi Jed,
>>> thank you for your reply. Two followup questions below:
>>>
>>> 2017-04-04 22:18 GMT+02:00 Jed Brown <jed at jedbrown.org>:
>>>
>>>> Ingo Gaertner <ingogaertner.tus at gmail.com> writes:
>>>>
>>>> > We have never talked about Riemann solvers in our CFD course, and I
>>>> don't
>>>> > understand what's going on in ex11.
>>>> > However, if you could answer a few of my questions, you'll give me a
>>>> good
>>>> > start with PETSc. For the simple poisson problem that I am trying to
>>>> > implement, I have to discretize div(k grad u) integrated over each FV
>>>> cell,
>>>> > where k is the known diffusivity, and u is the vector to solve for.
>>>>
>>>> Note that ex11 solves hyperbolic conservation laws, but you are solving
>>>> an elliptic equation.
>>>>
>>>
>>> I begin to understand. Petscs FVM methods don't provide a FVM library
>>> that can be used to implement the FV control volume approach (see Ferziger)
>>> for general CFD problems? They are around just because they have been used
>>> to tackle one or two specific problems, is this correct?
>>> I thought they could be used similar to the OpenFvm or OpenFoam libraries
>>> which seem to solve Poisson, Navier-Stokes, Euler and other problems. If
>>> such methods have not been prepared for Petsc, I'll just follow Ferzigers
>>> book and start my work on a lower level than I thought would be necessary.
>>> More work, more fun :)
>>>
>>
>> Yes, that is correct.
>>
>> As a side note, I think using FV to solve an elliptic equation should be a
>> felony. Continuous FEM is excellent for this, whereas FV needs
>> a variety of twisted hacks and is always worse in terms of computation and
>> accuracy. Hyperbolic problems are what FV is designed for
>> and I don't think I would ever support it for anything but that.
>>
>>   Thanks,
>>
>>     Matt
>>
>>
>>> > (My second question is more general about the PETSc installation. When I
>>>> > configure PETSc with "--prefix=/somewhere --download-triangle
>>>> > --download-parmetis" etc., these extra libraries are built correctly
>>>> during
>>>> > the make step, but they are not copied to /somewhere during the "make
>>>> > install" step.
>>>>
>>>> Where are they put during configure?
>>>>
>>>
>>> My bad, Petsc installation works as expected. But the build system that I
>>> am using is doing something weird. I'll have to find out, what's going
>>> wrong there, but it is not related to Petsc.
>>>
>>> Thank you!
>>> Ingo
>>>
>>>
>>>
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>>>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
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