During my PhD work, I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations.
My tables are discretized in temperature and pressure (which are the independent variables) as reported in the scheme below:
So I had to reconstruct an approximation of the general quantity $\phi$ for arbitrary couples of $p$,$T$ so that the CFD solver could retrieve them during the calculation.
Doing so with a simple Bilinear approach, works quite well for single species gas, but, when it comes to using mixtures I've observed really poor convergence rates and non-physical solutions.
The local bilinear approach it appears to be thermodynamic inconsistent: Maxwell relationships are not respected when thermodynamic quantities are independently interpolated.
On the other hand, using a consistent interpolation approach, such as a Hermite polynomial basis, everything works well without particular issues.
I would like to know if anyone has ever experienced such kind of problems, and if you have some ideas on the role of Maxwell relationships in non-ideal and compressible fluid dynamics.