Ingo Gaertner <[email protected]> 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 <[email protected]>: > >> On Wed, Apr 5, 2017 at 11:50 AM, Ingo Gaertner <[email protected] >> > wrote: >> >>> Hi Jed, >>> thank you for your reply. Two followup questions below: >>> >>> 2017-04-04 22:18 GMT+02:00 Jed Brown <[email protected]>: >>> >>>> Ingo Gaertner <[email protected]> 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 >>> >>> >>> >>> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> >>> Virenfrei. >>> www.avast.com >>> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> >>> <#m_-443598393346959692_m_-9031669297911553285_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> >>> >> >> >> >> -- >> 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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