Mathematical modeling and numerical solution of problems in process engineering, numerical methods for solution of ordinary and partially differential equations which describe processes in apparatuses and equipment. Optimization methods, regression analysis, parameter identification, process control and system stability. Computer simulation using software MATLAB and ANSYS CFD.

• Introduction into the mathematical modeling, problem analysis, types and selection of models, general approach of model assembling, post processing and validation, optimization.
• Representative equations and tasks of momentum, heat and mass transfer: continuity equation, balancing steady-state and transient systems, reaction kinetics, phase changes. Empirical models, regression models and artificial neural networks.
• Solution of ordinary differential equations describing dynamic behavior of basic process apparatuses and equipment, stability analysis of linear and non-linear systems, linearization, transfer characteristics of investigated system (production line equipment), identification, convolution, deconvolution, Fourier’s analysis (transformation).
• Numerical solution of ordinary differential equations, numerical stability, MATLAB.
• Basic types of controllers and control schemes, quality of the control process, optimization of the controller constants.
• Optimization and regression methods for evaluating experimental data and process models, one and multidimensional optimization, golden section method and other methods for searching minimum of model function. Least-squares method.
• Basic strategies for process and apparatuses control, e.g. chemical reactors, bioreactors, distillation columns, heat exchangers etc. Strategy of modeling and controlling the complex process line.
• Systems described by transport partial differential equations (parabolic, hyperbolic, elliptic). Navier – Stokes equation, Fourier’s equation.
• Numerical methods for solution of partial differential equations, finite-difference method (pressure drop in pipeline), method of characteristics (flow of compressible fluid in pipeline), method of weighted residuals (static analysis of truss construction). Scheme and application for basic types of equations, stability analysis.
• Finite volume method (2D solution of the fluid flow in diverging channel), solution of Navier-Stokes equations, SIMPLE algorithm.
• Turbulence modeling, different approaches of turbulence description (RANS, LES, DNS).
• Multiphase systems and various modeling approaches (VOF, Euler, Lagrange).
• Meshless methods, DEM (description of moving particles in fluid and their interactions).

• Study materials available at internal Moodle system: http://moodle.cvut.cz.
• Zienkiewicz O.C., Taylor R.L.: The finite element method, Vol. 3 – Fluid dynamics, Butterworth Heinemann, Oxford, 2000.
• Luyben W.L.: Process Modelling, Simulation, and Control for Chemical Engineers, 1974, 1990.
• Bequette B.W.: Process Control: Modeling, Design and Simulation, 2003.
• Roache, P. J.: Computational fluid dynamics. Rev. print. Albuquerque, N.M.: Hermosa Publishers, 1976.
• Wilcox D. C.: Turbulence Modeling for CFD, DCW Industries, 2006.