Mathematical modeling for industrial applications

• To produce a mathematical model for description of the industrial processes, developing in space and time, and involving transport of matter and energy by convection and diffusion, as well as chemical reactions;
• To formulate initial and boundary conditions for a mathematical problem applying relevant physical considerations;
• To learn and to be able of working with the differential balances. To formulate mathematical problems for the systems involving such balances. To select the solution methods for these problems;
• To develop the algorithms for solution of the systems of ordinary differential equations based on the standard library procedures;
• To implement such algorithms into the computer codes on modern programming languages;
• To apply the methods for qualitative analysis and numerical solution of the coupled systems of differential equations, including stiff problems;
• To analyze the obtained solutions in terms of the dimensionless parameters of the systems;
• To check stability of the systems and find the values of the critical parameters.

Teaching is built around a number of model examples, which broadly describe the statements of the problems with the chemical- and biochemical contents. The problems are solved numerically, applying programming as a tool. The possible model examples are (the choice may be different in the different years):

Modelling of the enzymatic hydrolyses

Modeling the chromatographic processes

Modeling of the diffusion through the coating

Modeling of adsorption separations

Modeling of the filtration of water containing solid particles

Courses on mathematical analysis, ordinary differential equations and basics of partial differential equations. Initial knowledge of programming.

“Learn by doing”. Assignments, short lectures.