Computer simulation of building materials production process

We consider the process of production of building materials based on the interaction of three reagents. To describe the nature and time of the technological process, we propose a new mathematical model. The mathematical model is an initial boundary value problem for a system of three nonlinear partial differential equations of the second order. The proposed mathematical model is a modification of the kinetic system of Godunov-Sultangazin equations used to describe the autocatalytic reaction of a three-component mixture. The Godunov-Sultangazin system is a system of equations of the first order, the addition of terms containing second derivatives makes it possible to formulate the problem more correctly and, moreover, to describe the process more accurately. It is proved that the proposed model solution satisfies the law of conservation of mass. The mathematical model under study is nonlinear, which explains the difficulty of obtaining its analytical solution. Therefore, we use numerical research methods to study it. For the numerical solution of the problem, a finite-difference method of the second order of accuracy is used. To obtain the characteristics of the solution, quadrature formulas of straight-angles and the spline approximation method are used. The numerical results obtained are presented. The results obtained are compared with the results obtained earlier for the discrete kinetic system of Godunov-Sultangazin.