Adaptation of the in situ adaptive tabulation (ISAT) procedure for efficient computation of surface reactions

In this article, the in situ adaptive tabulation (ISAT) procedure, originally developed [Pope, S. (1997). Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combustion Theory and Modeling, 1, 41-63] for the efficient computation of homogeneous reactions in chemically reacting flows, is adapted for the efficient computation of heterogeneous surface reactions. The main difference between the treatment of homogeneous and heterogeneous reactions is that heterogeneous reaction calculations require solution of a set of nonlinear algebraic equations at boundary faces/nodes, as opposed to the solution of an initial value problem, for which the original ISAT procedure was developed. The article first explains how the ISAT procedure is adapted for repetitive solution of a single nonlinear equation (scalar case), and subsequently presents the mathematical formulation for a system of nonlinear equations with multiple inputs and outputs (vector case). The new procedure is tested for catalytic combustion of a methane-hydrogen mixture on platinum using a reaction mechanism that involves 24 steps and 19 species (8 gas-phase and 11 surface-adsorbed). For this particular test case, the computational speed-up factor was found to be close to two orders of magnitude. Strategies to minimize memory requirements, while retaining optimum efficiency and accuracy are also outlined in the article.