Local Approximation of Two-Dimensional Tables of Thermophysical Data

The approximation of two-dimensional tables using local splines of the second order is proposed. Start point is the approximation for mixed derivative, which gives continuous functions for both partial derivatives. It is very important for tables of thermodynamic data, where besides the function it is required to know its partial derivatives. It is shown that constructed splines are monotonic, sign-preserving and convexity-preserving in corresponding area, where original function has these properties. The efficiency of the algorithm was verified for real equation of state Van-der-Vaalse type with phase transition.