Performance enhancing algorithms for computing thermodynamic equilibria

The rate of convergence of most numerical optimization methods can be accelerated by initial estimates that are near the final solution. Two relatively simple algorithms are presented that can improve upon initial estimates of traditional methods, and can thereby increase the computational performance of thermodynamic equilibrium calculations. The first algorithm improves upon traditional estimation techniques by providing initial estimates to a general solver that are much closer to the equilibrium values. The second algorithm is based on the strategic selection of phases to be exchanged when the number of thermodynamic degrees of freedom is zero. This algorithm enforces the Gibbs phase rule while also reducing the number of iterations required to establish a new assemblage of stable phases. Both algorithms have been found to significantly improve performance, especially when applied to systems with many system components or when the variation in the number of moles of the elements varies by a few orders of magnitude. Performance gains are particularly important when thermodynamic computations are integrated in large coupled multi-physics simulations.