1. Basic terms: system and its properties, structure and target behaviour; devices, processes, operations,
physical or chemical phenomena. Introduction to mathematical modelling: model, modelling,
mathematical modelling.
2. Classification of mathematical models, deterministic and stochastic models, empirical (statistical)
models and models derived on the base of natural relations (analytical models). Methods of
mathematical models obtaining. Mathematical structure of equations in mathematical models.
3. Statistical models. Regression calculation – evaluation of experimental data. Basic terms: least
squares method, standard error of estimation, coefficient of determination, standard error of coefficients,
ANOVA, t-test. Models of linear and non-linear regression. Multiple regression.
4. Analytical models. Phenomenological approach to mathematical modelling of processes – model
based on theory of transport phenomena.
5. Application of mathematical modelling: mathematical modelling of kinetics of subsequent chemical
reactions – theoretical background.
6. Application of mathematical modelling: mathematical modelling of diffusion processes in crystallize
materials (metallic alloys) – theoretical background.
7. Theoretical principles of mathematical modelling of fluid flow phenomena. Flow of real fluids. Laminar
and turbulent flow. Navier-Stokes equations and continuity equation. Mathematical models of
turbulence. Computational mesh. Discretization technique.
8. CFD software systems. The procedure of numerical simulation in CFD programme ANSYS FLUENT.
Preprocessing – geometry creation and generation of computational mesh, the definition of a physical
model, the choice of turbulence model, setting of the operational conditions, determination of material
properties and boundary conditions. Processing - Solving: the actual implementation of the calculation
(stationary, nonstationary), convergence of the solution. Postprocessing - evaluation of results.
Examples of using CFD programmes in practice.
9. Basic terms of process modelling, classification of models according to different criteria. Physical
modelling and its importance in various fields of science. System Similarity, the similarity constants.
The geometric, kinematic and dynamic similarity. Dynamic similarity of hydrodynamic systems. Basic
types of forces in hydrodynamics. Thermal similarity.
10. A complete physical equations, the basic equations, the criterial equations. Determination of
dimensionless parameters using dimensional analysis, practical examples of using of dimensional
analysis.
11. Determination of dimensionless parameters using method of similarity transformation of the basic
equations. Indicators of similarity. Similarity transformation of differential equations of the flow of real
viscous fluids. Comparison of both methods for determination of the similarity criteria. Approximate
physical modelling. Automodelling. Physical meaning of some similarity criteria.
12. Fundamentals of flow reactors - hypothetical models of flow, plug flow, perfect mixing. Real reactor.
Theoretical retention time. Curve C, curve F. A combined flow model, mean retention time, short-flow,
dead volume. Dispersion flow model.
13. Methods for determination of retention times, the impulse-response method, the RTD curves, flow
visualization. The principles of construction of physical models. Basic experimental techniques in
physical modelling of flow of liquid metals. Selected electronic information resources in the area of
mathematical and physical modelling.
physical or chemical phenomena. Introduction to mathematical modelling: model, modelling,
mathematical modelling.
2. Classification of mathematical models, deterministic and stochastic models, empirical (statistical)
models and models derived on the base of natural relations (analytical models). Methods of
mathematical models obtaining. Mathematical structure of equations in mathematical models.
3. Statistical models. Regression calculation – evaluation of experimental data. Basic terms: least
squares method, standard error of estimation, coefficient of determination, standard error of coefficients,
ANOVA, t-test. Models of linear and non-linear regression. Multiple regression.
4. Analytical models. Phenomenological approach to mathematical modelling of processes – model
based on theory of transport phenomena.
5. Application of mathematical modelling: mathematical modelling of kinetics of subsequent chemical
reactions – theoretical background.
6. Application of mathematical modelling: mathematical modelling of diffusion processes in crystallize
materials (metallic alloys) – theoretical background.
7. Theoretical principles of mathematical modelling of fluid flow phenomena. Flow of real fluids. Laminar
and turbulent flow. Navier-Stokes equations and continuity equation. Mathematical models of
turbulence. Computational mesh. Discretization technique.
8. CFD software systems. The procedure of numerical simulation in CFD programme ANSYS FLUENT.
Preprocessing – geometry creation and generation of computational mesh, the definition of a physical
model, the choice of turbulence model, setting of the operational conditions, determination of material
properties and boundary conditions. Processing - Solving: the actual implementation of the calculation
(stationary, nonstationary), convergence of the solution. Postprocessing - evaluation of results.
Examples of using CFD programmes in practice.
9. Basic terms of process modelling, classification of models according to different criteria. Physical
modelling and its importance in various fields of science. System Similarity, the similarity constants.
The geometric, kinematic and dynamic similarity. Dynamic similarity of hydrodynamic systems. Basic
types of forces in hydrodynamics. Thermal similarity.
10. A complete physical equations, the basic equations, the criterial equations. Determination of
dimensionless parameters using dimensional analysis, practical examples of using of dimensional
analysis.
11. Determination of dimensionless parameters using method of similarity transformation of the basic
equations. Indicators of similarity. Similarity transformation of differential equations of the flow of real
viscous fluids. Comparison of both methods for determination of the similarity criteria. Approximate
physical modelling. Automodelling. Physical meaning of some similarity criteria.
12. Fundamentals of flow reactors - hypothetical models of flow, plug flow, perfect mixing. Real reactor.
Theoretical retention time. Curve C, curve F. A combined flow model, mean retention time, short-flow,
dead volume. Dispersion flow model.
13. Methods for determination of retention times, the impulse-response method, the RTD curves, flow
visualization. The principles of construction of physical models. Basic experimental techniques in
physical modelling of flow of liquid metals. Selected electronic information resources in the area of
mathematical and physical modelling.