Cubic and Spline Interpolation Methods
Cubic (Akima) and Spline are among the interpolation options that are available for use with profile methods and expressions in Simcenter STAR-CCM+.
Cubic (Akima) Interpolation
Cubic (Akima) interpolation provides a piecewise cubic curve fit that consistently passes through the input points. The derivatives of the curve are estimated at each input data point using a 5-point approximation scheme.
For each segment between the data points, two pre-computed derivatives and two known spline values are used for building a unique cubic curve. If an insufficient number of input points are provided (less than 4), linear interpolation is performed instead.
By contrast, spline interpolation has a continuous first derivative and possibly discontinuous second derivative.
Spline Interpolation
Spline interpolation fits a spline through the provided data points, then samples that spline more finely than the original data, and stores the sampled points. When interpolation is required, it interpolates linearly between the sampled points.
This method was used in versions of Simcenter STAR-CCM+ prior to 2021.3. However, you are advised to use the newer Cubic (Akima) when setting up tabular methods or expressions.