Performance of algorithms for calculating the equilibrium composition of a mixture of gases

Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensional finite-difference computer codes require the equilibrium gas composition as an input. Because the equilibrium problem must be solved a large number of times, it is essential that the equilibrium solver be fast and reliable. An existing solver is a variant of the Gauss-Seidel technique, and its performance can be predicted and quantified. It is relatively fast, but can be unreliable. By contrast, Newton's method is slower but more reliable. A hierarchical algorithm, in which recourse is made to Newton's method if Gauss-Seidel iteration fails, is shown to combine the speed of Gauss-Seidel and the reliability of Newton. The hierarchical solver has been incorporated into the CONCHAS computer code. The reliability of the code is improved, and there is a decrease in the amount of computer time required. The new algorithm has not failed during production runs of CONCHAS, but it has failed to find the solution of some special test problems.