Simcenter STAR-CCM+ How does Simcenter STAR-CCM+ interpolate data in Laminar Flame Speed (LFS) data in a table?

Laminar Flame Speed (LFS) is a critical input for combustion models in Simcenter STAR-CCM+, such as ECFM-3Z, ECFM-CLEH, CC-TFC, and the ISSIM ignition model. LFS can be determined in two ways:

• Correlation: Simcenter STAR-CCM+ offers built-in correlations like Gulder LFS or Metghalchi LFS to calculate LFS based on the fuel properties and operating conditions.
• Precomputed LFS table: Alternatively, users can import a precomputed LFS table file. These tables, often containing LFS values as a function of equivalence ratio, EGR more fraction, gas pressure and unburnt gas temperature, are available for download from Siemens Support Center or can be created by the user.

In regards to the data source from LFS table, Simcenter STAR-CCM+ retrives and interpolates the LFS data from the table file based on the order it is stored in the file to determine the appropriate LFS value. Simcenter STAR-CCM+ essentially performs multi-dimensional reduction for the linear interpolation, which follows the order of the data stored in the LFS table file. The order of the multi-dimensional reduction for the linear interpolation has been hard-coded into the software; therefore users will not be able to change the order of the interpolation. So if the data in the LFS table file is stored in a different order, the retrieval and the order of the multi-dimensional reduction for the linear interpolation of the data will follow that order. The developers of Simcenter STAR-CCM+ confirmed that the interpolated LFS value hypothetically should be the same regardless the order of the data in the table file. A useful resource from the Wikepedia: Bilinear Interpolation confirms it:

The result of bilinear interpolation is independent of which axis is interpolated first and which second. If we had first performed the linear interpolation in the y direction and then in the x direction, the resulting approximation would be the same.

So what does Simcenter STAR-CCM+ do when one of the four independent variables, e.g., unburnt gas temperature, is beyond the range of the data in the LFS table file? Simcenter STAR-CCM+ will use the near MIN/MAX data for the interpolation. So if the unburnt gas temperature of a computational cell is 4000K and the data in the table file for independent variable: unburnt gas temperature is ranging from 300K to 2800K, Simcenter STAR-CCM+ will use the value 2800K to perform the multi-dimensional interpolation to obtain the LFS value for that computational cell.