Computer Research of Building Materials

Abstract

A computer study of the technological processes for the production of building materials based on the use of reversible autocatalysis reactions is carried out. For the mathematical description of the process of autocatalytic reactions, mathematical models are used, described by a initial-boundary problems for the Carleman system. The considered mathematical model describes the autocatalysis reaction under the following assumptions: the rate of decrease in the density of positive ions is proportional to the square of the deviation of the density of positive ions from the equilibrium state, the rate of decrease in the density of negative ions is proportional to the square of the deviation of the density of negative ions from the equilibrium position and the law of conservation of the total charge of the system including liquid solution. This mathematical model is non-linear, therefore numerical methods are used for its study. For a numerical solution of the initial-boundary value problem for the Carleman system, a finite-difference method of the second order of accuracy is used. For the numerical investigation of the solution obtained, linear interpolation and spline interpolation are used. A numerical study is made on the dependence of the chemical reaction time from the parameters of the model and various initial conditions.