Axisymmetric extensions to Tomboulides class
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These changes include * adding a radius multiplier to many operators * a function to evaluate the curl of a field (and thus allow us to get the double curl of the velocity) in the axisymmetric case (NB: For now this is a separate function, but it could be merged with the 2D variant). * forms and integrators for "extra" terms that arise in the axisymmetric case
This is necessary for a pipe flow test case, which is first case where we will exercise the axisymmetric extensions.
Only 1 interpolated inlet is supported, but with previous version of this check, code would exit for cases with 1 inlet that wasn't an interpolation inlet.
This includes * An input file flag to disable "numerical integration" (NB: here "numerical integration" really means under-integrating using the solution nodes as quadrature points. This is a problem in the axisymmetric case b/c it can lead to quadrature points on the axis, where r=0. This leads to a singular mass matrix.) * Including radius factors that were missed in the initial axisym commit. With these changes, the fully-developed-pipe flow case runs and produces a reasonable looking result with linear elements, although no grid convergence has been done yet, so we need more systematic testing.
Obviously only contributes when u_{\theta} is not zero, which isn't
supported yet, but is on the way.
Many limitations still, in particular, the convection terms in the utheta eqn are missing and variable dynamic viscosity terms are missing.
This is the most basic case I can think of that touches axisymmetric with swirl.
Currently virtually untested, since both pipe and Taylor-Couette tests use constant viscosity. So, we know the new terms do not destroy our previous results, but that is about it. Need to find/design a test for these terms.
To avoid false failures due to relative errors at places where the velocity is essentially zero.
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The PR adds support for axisymmetric flow simulations in the
Tomboulidesclass.