1. Thermodynamics & CFD • Harris et al (1996): … numerical solution ... in a flow geometry of interest, together with subsidiary sets of equations … transport, diffusion and reaction of chemical species. • Kuipers and van Swaaij (199?): … The SIMPLE algorithm (Patankar, 1980) … forms the basis of … PHOENICS, FLUENT, FLOW3D … additional transport equations can be added with relative ease.

2. SIMPLE • The solver controls V, p, E, m as functions of and t,x,u; • This gives four dependent variables, which is one too many compared to thermodynamic theory; • Thermodynamic relation p = p(V,E,m); • Is there a way to correct this flaw without rewriting the solver(?)

3. Incompressible flow • The solver controls U,b (and V, p, Ek , Ep ) as functions of and t,x,u; • Two dependent variables in accordance with thermodynamic theory;

4. Compressible flow • The solver controls V, U,b (and Ek , Ep ) as functions of and t,x,u (barycenter); • Three dependent variables in accordance with thermodynamic theory;

5. Compressible flow (continued) • The solver controls extensive variables xi; • Thermodynamic EOS supplies intensive properties ci needed in transport equations and alike; • Bilinear coupling: • Reformulation into from “Lagrange” to “Euler” cordinates?