Local Approximation of Two-Dimensional Tables on Nonuniform Grids

The approximation of two-dimensional tables on nonuniform grids using local splines is proposed. Biquadratic polynomial approximation allows obtaining continuous first partial derivatives. It is very important for tables of thermodynamic data, where besides the function it is required to know its partial derivatives. Constructed splines are monotonic, sign-preserving and convexity-preserving in corresponding area, where original function has these properties. These properties were investigated on set of important one dimensional cases for smooth functions, functions with break and step. The efficiency of the algorithm was verified for real equation of state of iron with phase transition.