8.5.3 Steady Laminar Flamelet Automated Grid Refinement

By default, 1D flamelet grids are discretized by clustering a fixed number of points about the stoichiometric mixture fraction, which is approximated as the location of peak temperature. ANSYS FLUENT also has the option for Automated Grid Refinement of steady flamelets, where an adaptive algorithm inserts grid points so that the change of values, as well as the change of slopes, between successive grid points is less than user specified tolerances.

When using automated grid refinement, a steady solution is calculated on a coarse grid with a user specified Initial Number of Grid Points in Flamelet (default of $8$). At convergence, a new grid point is inserted midway between a point $i$ and its neighbor $i+1$ if,

where $v_i$ is the value for each temperature and species mass fraction at grid point $i$, $\epsilon_v$ is a user specified Maximum Change in Value Ratio (default of $0.5$), and $v_{max}$ ( $v_{min}$) are the maximum (minimum) values over all grid points.

In addition a grid point is added if,

where the slope $s_i$ is defined as,

In Equations  8.5-3 and 8.5-4, $\epsilon_s$ is a user specified Maximum Change in Slope Ratio (default of $0.5$), $s_{max}$ ( $s_{min}$) are the maximum (minimum) slopes over all grid points, and $f_i$ is the mixture fraction value of grid point $i$.

The refined flamelet is reconverged, and the refinement process is repeated until no further grid points are added by Equations  8.5-2 and 8.5-3, or the user specified Maximum Number of Grid Points in Flamelet (default of $64$) is exceeded.