Modeling Of Catalytic Reactors As Elliptic Problems With Essential Border Singularities

Abstract

The modeling of catalytic reactors as sets of elliptic problems with boundary conditions
of Dirichlet, Neumann, and mixed types, is studied. The main issue in the modelisation and
solution procedure is the nonlinearity and presence of boundary singularities that are essential
to these systems.
After the introductory items, the main objective of this article is treated: the modeling of
catalytic reactors as sets of elliptic problems with essential border singularities. A system of
elliptic (stationary) advection-diffusion equations with boundary conditions of Dirichlet, Neumann
and, also, of really demanding essential singular nonlinear Robin type is posed and an
algorithm for their numerical solution is proposed.
This second set of examples are associated to problems drawn from Chemical Engineering
(Simplified Catalytic Reactors) with the aim of providing reasonable solutions and acceptable
a posteriori error estimates. The modeling and simulation of the reactor is also an issue in this
article.
More research is still needed, in particular in the transient initialization modeling by parabolic
equations, but the methods appear to be powerful and simple tools for obtaining accurate finite
element solutions and error estimation and is able for adaptivity of meshes.
It is interesting to note that, including convex polygonal domains, the method is efficient and
it appears to be not related to the order of the numerical algorithm.