The test case, input.cvar in FlameSheet, can be run after using the script and instructions in NatLabRockies/cmlm#5 to create the 2D chemtable and then copying the chemtable and PMF data files over the FlameSheet directory.

Test case (Exec/RegTests/Flamesheet/input.manifold.cvar) can be run by first executing the python get_pmfdat_and_ctable_withvar.py in the cmlm repo, then copying the files data/prem_drm19_phi1_p1_t298.ctb and data/prem_drm19_phi1_p1_t298_mani_filter2.344e-03.dat to the FlameSheet directory. The FlameSheet case needs to be compiled with USE_MANIFOLD=TRUE and Manifold_Dim = 2.

I've realized that I did not include the production rate in the variance equation (see below). To include this we will need to evaluate scalar gradients, but once we have those it should be very straightforward to add.

Merging this for some work that depends on it, but it should be treated as an "under active development" feature.