For most problems, these new default tolerances for both time stepping and
steady state solves are more likely to converge than tighter tolerances, but
still give well-resolved results. Tighter tolerances are required in some cases,
e.g. when evaluating sensitivity coefficients by finite difference.
Previously, the first species was always used, which could cause problems with
negative mass fractions in cases where the first species has a mass fraction
near zero.
Implements the radiation model of Liu & Rogg (1991). Optically thin limit,
gray-gas approximation using Planck mean absorption coefficients. Considers
emissions from CO2 and H2O, with the temperature-dependent absorption
coefficients calculated using polynomial fits to results from RADCAL
(Grosshandler, 1993).
In combination with the previous commit, this significantly improves the
convergence behavior of the solver when using multicomponent transport
properties. In many cases, the solver is now able to directly solve the
multicomponent problem directly from the mixture-averaged solution without any
timestepping.
Change the formulation of multicomponent diffusion fluxes to avoid using the
equivalent Fickian diffusion coefficient. That formulation leads to negative
diffusivities for some species at some grid points, which generate numerical
instabilities while timestepping. This formulation produces a more dense
Jacobian, but with a much better eigenvalue spectrum.
Calling solve() again after a successful solution no longer automatically
triggers a Jacobian update. This enables relatively efficient sensitivity
analysis by sequentially perturbing the reaction multipliers and re-solving
the system. Since the perturbed system is close to the orignal, the solution
can be found after only a few steps, even when using the original Jacobian.
The failures were caused when attempting to restore the tolerance vectors, which
have a value for each species. Since these tolerances are usually the same for
all species, the last value in the array can be used to extend the array to the
required length.
Also add some tests for this feature.
