A methodology for solving chemical equilibrium systems (Q1821509)

This paper describes a methodology for solving chemical equilibrium systems. The methodology is especially appropriate when many systems with the same structure must be solved quickly, as in finite-difference models of fluid flow and combustion. The approach features identifying a ''canonical form'' for such systems and exploiting this canonical form to effect a preliminary algebraic reduction. Then numerical scaling and iterative solution techniques are evoked. Both homotopy continuation and a variant of Newton's method are effective solution methods. This methodology is a significant advance over previous approaches to solving chemical equilibrium systems. The problem of solving such systems has heretofore been regarded as challenging; solution techniques have tended to emphasize case-by-case analyses and hit-or-miss numerical methods. We show that the problem can be solved by a unified approach, quickly and reliably.