During my PhD work I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations. CFD simulations consist in the numerical solution of Navier-Stokes equations (with opportunes modeling approximations).
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 use mixtures I've observed really poor convergency 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 consistant interpolation approach, such as Hermite polynomial basis, everything work well without particular issues.
I would like to know if anyone have 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.
Thank you in advance.