1. Role of CFD in design of fluid machines, advantages and limitations of computational modeling. Motivating presentation of CFD applications.
2. Basic differential equations of fluid mechanics, mathematical classification of these equations, necessity of numerical solution.
3. Approaches to discretization of partial differential equations (finite differences, volumes, elements). Finite volume method (FVM).
4. Application of FVM to 1D and 2D diffusion. Solution of the systém of equations. Convergence.
5. Unsteady problem. Explicit, implicit scheme.
6. Advection - diffusion problem, algorithm SIMPLE.
7. Flow in rotating frame of reference (multiple reference frame, mixing plane, sliding mesh), multiphase flow ; basic principles.
8. Turbulence, possibilities of computational solution. Statistical analysis. Reynolds equations. Turbulent stress tensor. Problem of the equation systém closure. Boussinesque hypothesis.
9. Turbulence models (zero, one, two equation models, Reynolds stress model). Large eddy simulation. Direct numerical simulation.

10. Advanced turbulence models (scale resolved, hybrid)
11. Near wall modeling (wall functions, two layer approach). Visualization in CFD environment.
12. Shape optimization of fluid elements, Geometry parametrization, objective function definition, interconnecting of optimization and CFD. Principles of some optimization methods.
13. Integration of CFD process of research and development.  Presentation on the real example of fluid machine or element (together with presentation of the research engineer from industry).