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There are many software packages for the finite element method, of which the most popular are listed e.g. on Wikipedia. When it comes to the finite volume method, I'm not aware of any similarly comprehensive list. In fact, the only software package I'm actually aware of is OpenFOAM. Do you know any alternatives?

(I'm mostly interested in software capable of describing (a system of) general advection-diffusion-reaction PDEs, not just a specific model such as Navier-Stokes. But if there are good extensible Navier-Stokes solvers, they can be listed as well.)

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    $\begingroup$ I am aware of FiPy, but have not used the package or even finite volume methods in general. $\endgroup$ – knl Jan 31 '18 at 10:18
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    $\begingroup$ SU2 is another opensource FVM package. If you're also interested in commercial options, Ansys CFX and Fluent both use the FVM $\endgroup$ – cbcoutinho Jan 31 '18 at 13:40
  • $\begingroup$ see this question $\endgroup$ – GoHokies Jan 31 '18 at 18:30
  • $\begingroup$ @cbcoutinho Although SU2 seems to be focused on a specific application. Although its authors claim that "it is extensible (and has been extended) to treat arbitrary sets of governing equations such as electrodynamics, chemically reacting flows, and many others", there isn't anything to support that or even pointers to tutorials/examples showing how it could be done. And commercial packages are out of interest entirely. $\endgroup$ – Jakub Klinkovský Jan 31 '18 at 22:03
  • $\begingroup$ @GoHokies Unfortunately the answers for that question do not provide the overview of the numerical methods used by the software. Otherwise, there are several useful suggestions, so thanks for the comment. $\endgroup$ – Jakub Klinkovský Jan 31 '18 at 22:19
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Have a look at Pyclaw. This library has been around for quite a while and is fairly robust. It offers:

  1. Implementations of several Godunov-type methods and Riemann solvers in 1/2/3D.

  2. Adaptive mesh refinement (via AMRclaw).

  3. Support for parallel computing - among other things, it ties-in nicely with PETSc, as shown here.

  4. Support for some geophysical flow problems (e.g., shallow water) via Geoclaw.

  5. Comprehensive documentation.

Some of the authors / contributors to the library are active on this forum.

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