Application of hyperbolization in the diffusion model of a heterogeneous process on a spherical catalyst grain

The article investigates the application of hyperbolization for parabolic equations to the material and thermal balances' equations for a mathematical model of oxidative regeneration of a spherical catalyst grain with detailed kinetics. The initial spherical grain model is constructed using a diffusion approach. It is a nonlinear system of differential equations in a spherical coordinate system. The material balance of the gas phase is described by diffusion-convection-reaction equations with source terms compiled for concentrations of substances of the gas phase; the balance of the solid phase is represented by nonlinear ordinary differential equations. The thermal balance equation of the catalyst grain is the thermal conductivity equation with an inhomogeneous term corresponding to the grain heating during a chemical reaction. Slow processes of heat and mass transfer in combination with fast chemical reactions lead to significant difficulties in the development of a computational algorithm. Hyperbolization of the parabolic equations is applied to avoid the computational complication. It consists in the introduction of a second time derivative multiplied by a small parameter, in order to expand the stability area of the computational algorithm. An explicit three-layer difference scheme is constructed for the modified model. It is implemented in the form of a software module. The convergence analysis of the developed algorithm is presented. A comparative analysis of the new computational algorithm with the previously constructed one is carried out. The advantage of the new algorithm while maintaining the order of accuracy is shown. The result of the implemented new algorithm is the profiles of the distribution of temperature and substances along the radius of the catalyst grain.