Basic concepts of computational fluid dynamics: Introduction to CFD. Descriptions of the main approaches used in CFD: 1D, 3D. Mathematical classification of the types of flows (compressible, incompressible, viscous, non-viscous, real or ideal gas).
Space discretization: grids for finite difference methods and for finite volume methods. Structured and unstructured grids, tetrahedral and hybrid calculation grids. Advanced meshing strategies: overset meshes.
Turbulence and its modeling: Physical meaning of turbulence. Approximation levels for the modeling of turbulent phenomena. RANS turbulence models.
Finite difference schemes: discretization of first and second derivative in space for convection/diffusion
problems. Fist order and second order methods.
Finite volume schemes: Numerical approximations of surface and volume integrals. Interpolation techniques and accuracy of the different methods. Implicit and explicit integration into time.
Solution of systems of linear equations: direct and iterative methods, elimination of Gauss, LU decomposition, method of conjugated gradients and multigrid methods.
Solution of PDE problems: definition of staggered and co-located grid SIMPLE algorithm and PISO algorithm.
INTERNAL COMBUSTION ENGINES PART
Moving grid techniques: formulation of the conservation equations for control volumes with moving boundaries. Deformation of the mesh by interpolation. Movement of the calculation grid with removal and addition of cell layers. Relative movement of grids through "sliding interface" and "Generic Grid Interface" approaches. Application of mesh deformation and remapping of fields between different calculation grids.
1D methods for simulating C.I engines: State of the art. Methods for finite differences and finite volumes 1D. Method of characteristics for non-stationary flows. Resolution of the boundary conditions by method of the characteristics. Integration method of characteristics with finite difference schemes. Modeling of reacting flows.
Spray modeling: Lagrangian transport equations. Break-up models, evaporation and collision of liquid drops. Introduction to the "Finite Area" (FA) discretization. Modeling of the process of formation and evaporation of "wall film".
Flow patterns in turbomachinery: projection of equations of motion on inter-palar and meridional surfaces.
Two-dimensional flow solution around airfoils, cascades, and rotors: domain definition, grid topology, periodicity, boundary conditions for subsonic and supersonic flows. Application of turbulence models and their effects on profile losses and heat exchange. Mixing planes for multi-row configurations.
Flow solution on the meridional surface: generalized radial equilibrium. Methods based on the curvature of the flow lines. Two-dimensional throughflow methods.