Improved iteration scheme for partial equilibrium flow (Q1083974)

A numerical method for partial equilibrium flow was recently described [the first author and \textit{L. D. Cloutman}, ibid. 39, 405-417 (1981; Zbl 0469.76068)]. The heart of the method is a quadratic iteration scheme in which the progress increment for equilibrium reaction s is obtained from the equilibrium constraint for reaction s alone. The scheme therefore converges best when the equilibrium reactions are weakly coupled, which can frequently be achieved by a judicious choice of the independent equilibrium reactions. The new iteration scheme consists of the following ingredients: (a) preconditioning of the equilibrium constraints conditions to make them more nearly linear in the progress variables, (b) application of a one-step Gauss-Seidel-Newton iteration to the preconditioned system, followed by (c) switching to a full Newton-Raphson iteration if the simpler Gauss-Seidel-Newton iteration fails to converge in a specified number of steps. If the equilibrium reactions are weakly coupled, convergence usually occurs before the full Newton-Raphson iteration is called into play. However, if the reactions are not weakly coupled the interaction between them is properly accounted for by the matrix inversion in the Newton-Raphson procedure.