Implementation of sparse matrix algorithms in an advection–diffusion–chemistry module

A two-dimensional advection–diffusion–chemistry module of a large-scale environmental model is taken. The module is described mathematically by a system of partial differential equations. Sequential splitting is used in the numerical treatment. The non-linear chemistry is most time-consuming part and it is handled by six implicit algorithms for solving ordinary differential equations. This leads to the solution of very long sequences of systems of linear algebraic equations. It is crucial to solve these systems efficiently. This is achieved by applying four different algorithms. The numerical results indicate that the algorithms based on a preconditioned sparse matrix technique and on a specially designed algorithm for the particular problem under consideration perform best.