Numerical solution of one inverse problem for a diffusion model of a chemical-technological process

Abstract

A chemical-technological process taking place in a chemical reactor with a chemical reaction of the second order is considered. A one-dimensional one-parameter diffusion model of the hydrodynamic flow in the reactor is proposed for the mathematical description of this process. Within the framework of the proposed model, the inverse problem is posed to determine the concentration of the selected reagent in the incoming flow, ensuring the implementation of a predetermined hydrodynamic regime at the reactor outlet. A discrete analogue of the inverse problem is constructed and the resulting difference problem is presented as a variational problem with local regularization. A special representation is proposed for the numerical solution of the variational problem. As a result, an explicit formula is obtained for determining the approximate concentration of the selected reagent in the incoming stream. The effectiveness of the proposed method is illustrated by numerical calculations for model problems