Mass conservative, positive definite integrator for atmospheric chemical dynamics

Air quality models compute the transformation of species in the atmosphere undergoing chemical and physical changes. The numerical algorithms used to predict these transformations should obey mass conservation and positive definiteness properties. Among all physical phenomena, the chemical kinetics solver provides the greatest challenge to attain these two properties. In general, most chemical kinetics solvers are mass conservative but not positive definite. In this article, a new numerical algorithm for the computation of chemical kinetics is presented. The integrator is called Split Single Reaction Integrator (SSRI). It is both mass conservative and positive definite. It solves each chemical reaction exactly and uses operator splitting techniques (symmetric split) to combine them into the entire system. The method can be used within a host integrator to fix the negative concentrations while preserving the mass, or it can be used as a standalone integrator that guarantees positive definiteness and mass conservation. Numerical results show that the new integrator, used as a standalone integrator, is second order accurate and stable under large fixed time steps when other conventional integrators are unstable.