## Some Tips for Table Generation

Two ways to generate solutions for the unstable middle branch:

(1) repeatedly compute solutions near the extinction limit and “hope” one jumps and converges to the middle branch. Not scientific but actually fairly efficient.

(2) use `arclengthcontinuation`

, which attempts to follow the curve by modifying the start profile. Some people have found this to be somewhat less efficient, but others have found it to be more foolproof.

## Interpolation in FlameMaster

If you have a value (e.g. stoichiometric Z) from which you need to interpolate all other variables, use

```
LT -s <name of blank file> -l Z,<mixture fraction value> <solution files>
```

You need to create this blank file first, otherwise it will report error.

## Some Tips for Result-Check of Table Generation

(0) Anything below 1400K (except the lower branch) is not very physical, and no need to take a lot of efforts to generate them: e.g. lower part of the middle branch, and small chi_st with large radiation.

(1) Plot a S-curve of C_st vs chi_st based on the data of upper and middle branches. Each branch should be monotonic, and upper branch should approach unity when chi_st is approaching zero. Sometimes, the middle branch could have some kinks, then just not include those data points in the table generation and let the interpolation to smooth them out.

(2) Check individual flamelets to ensure that there are not substantial shifts in mixture fraction space and that the Lewis numbers at the bottom are indeed what you want (e.g. unity).

(3) Try to have a gap in stoichiometric temperature not larger than 50K or so, if possible.

(4) Finally, use Paraview or Tecplot to check the 3D image of the chemtable to see whether there is some kinks/non-smoothness, and whether every quantity is reasonable.

(5) If the chemTable size generated is too large, the supercomputer cluster (such as the Hyperion Cluster) node could have insufficient memory to read the chemTable. In this case, you can consider reducing the number of points for the chemTable dimensions. For RFPV, four dimensions are used: Z (mean mixture fraction), Z” (variance of mixture fraction), C (progress variable) and H (radiation variable). When reducing the number of points, the significance of these variables: Z > C & H > Z”. In other words, you should first consider to reduce the number of points for Z”.