Preconditioning for the Dynamic Simulation of Reaction-Transport Systems

This paper presents an investigation of preconditioning techniques for the transient simulation of reaction-diffusion systems that are commonly encountered in chemical process design applications. Three model-based preconditioners were proposed. Their performance was compared with that of a standard incomplete LU decomposition based preconditioner (P1). Two of the model-based preconditioners, P2 and P3, were constructed using only the transport part of the reaction-diffusion model: One of them was calculated using numerical differentiation while the other was based on analytical formulas. Since the transport properties are commonly assumed to be constant in transient numerical simulations, the resulting preconditioners are time-independent and need to be calculated only once, at the beginning of the simulation, and thus the efficiency of the simulation is significantly improved. The preconditioner P4 was constructed by adding chemical reaction contributions, updated only when necessary during the entire transient simulation. The numerical results for several test cases show that P4, by adding reaction correction terms, is more effective in improving the speed of the reactor simulation than the other two while maintaining the advantages of easy construction and low computational cost. In addition, it was demonstrated that the preconditioner P4 can also be used as an approximated Jacobian matrix for Newton's iteration, which may improve the efficiency of the simulation even further.