Development of an algorithm based on space refinement to solve a system of parabolic PDE’s.

The objective of this work is the development of a space refinement algorithm based on the method of lines to solve systems of non-linear parabolic partial differential equations. The technique is applied for steady state and dynamic studies of a common chemical engineering system, a fixed bed reactor, described by a set of two partial differential equations with highly non-linear exponential terms. The algorithm developed aims the improvement of the solution in areas where high values of the space error indicator are detected. That improvement is done in certain subintervals through the calculus of the solution in points resulting from successive divisions of the discretization step. The proposed algorithm showed good efficiency in solving in transient state the system mentioned, allowing the achievement of good quality solutions in relatively small times