# Implications of thermodynamic inconsistency in CFD calculations

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.

• Please provide a definition of CFD. – Bob D Nov 15 '19 at 16:46
• Thank you Bob, I've slightly modified the post so to give a really brief explication on what is intended for CFD. – iterrate Nov 15 '19 at 20:38
• I think you may need to offer a bounty to get responses on this one. It's probably way over the heads of most folks. Good luck! – Bob D Nov 15 '19 at 21:19
• Unfortunately I don't have the privilege to do so yet – iterrate Nov 15 '19 at 21:26
• IMO you may get better feedback on the Computational Science SE than here. – Martin C. Nov 15 '19 at 21:35