Application of adaptive methods based on finite difference discretizations in the simulation of a tubular reactor system

In this paper two adaptive algorithms are presented for the solution of systems of evolutive one-dimensional Partial Differential/ Algebraic Equations (PDAEs). The temporal integration is coupled with a spatial adapting strategy. The identification of the spatial subdomains. where a regridding technique is introduced, is done through the comparison of the solutions computed with two fixed grids of different sizes. The subproblems generated are solved by two adaptive strategies: the Grid Refinement Method (GRM), that promotes the refinement of the subgrids detected in the previous step, and the Moving Mesh Method (MMM) includes an additional differential equation for the nodal mobility. The two algorithms proposed were successfully applied to the solution of an nonisothermal tubular reactor pseudo-homogeneous model described by two PDEs referring to reagent concentration and system temperature dynamics. The performance of each algorithm is compared to the results obtained by [3], based on the application of a formulation of the Moving Finite Elements Method, with cubic Hermite polynomials approximations