deal.II supports continuous and DG finite elements but is not a finite
volume library. There are many people using deal.II for CFD though.
Discontinuous Galerkin can be seen as a generalization of finite
volumes to higher order. Some things we can not do is arbitrary types
of cells (pyramids, prisms, etc.), which are often used in industrial
CFD applications.
Most applications use deal.II with implicit time discretization and
that is what a lot of the features are tailored to. So if you are
looking to do finite volume, explicit time stepping for turbulent flow
around an airplane, deal.II might not be your method of choice.
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--
Timo Heister
http://www.math.clemson.edu/~heister/