Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: Effect of the chemistry on the choice of numerical algorithm: 2. Numerical Results

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Abstract
This paper is the second in a two‐part series which studies the efficiency of several algorithms for solving the problem of multicomponent mass transport with equilibrium chemical reactions. In particular, the relative efficiency of competing algorithms is evaluated as a function of the nature of the chemistry. The first, formulation A, introduces the total soluble concentration of each component as the primary dependent variable. The second, with variants B and C, introduces the total component concentration, aqueous plus all solid forms, as the primary dependent variable. Finite element discretization in space and a single‐step, implicit time marching scheme reduces the problem to a set of nonlinear algebraic equations in each time step. Several versions of Newton‐Raphson iteration and Picard iteration are evaluated for the basic formulations by studying a set of single‐ and three‐component problems. The specific cases studied are each designed in order to emphasize a particular aspect of the equilibrium chemical reactions. Results indicate that overall, a modified Newton‐Raphson iteration is the most efficient solution strategy for the range of problems considered.