Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures.

A relatively succinct set of property calculations can be used to construct efficient (in memory and speed) numerical approximations of that function in a rectangular domain. Through the use of adaptive subdivision with quadtrees and bi-Chebyshev expansions in each leaf, the function can be practically represented to the order of the noise in the function to be approximated. A further benefit is that evaluation of the approximation is noniterative and thus cannot fail to converge (a relatively common problem in thermophysical property libraries, especially for mixtures). Evaluation of the approximation function requires only a few bisection steps to identify the leaf of interest such that evaluation of the approximation data structure takes less than a microsecond. The technique is demonstrated by application to the vapor-liquid-equilibria evaluated with two different models (COSMO-SAC activity coefficient model and multifluid model). For the more expensive COSMO-SAC case, the approximation function is more than 2000 times faster to evaluate, and deviations in pressure are less than a part in 10 which is practically equal to the iteration convergence criterion.