Lectures: 1. Basic equations of fluid mechanics. Lagrangean and Eulerian description, transport and localization theorems, balance laws, constitutive relations, equations of motions, simplified models. 2.-3. Advection-diffusion transport equation. Boundary and initial conditions. Finite volume method. Stability of time discretizations. 4. Finite element method for advection-diffusion equation. Stabilization for dominating advection. Discontinuous Galerkin method. 5. Stokes system. Boundary conditions, weak formulations. Finite element method, stability conditions. 6. Navier-Stokes equations. Weak formulation, finite element method, linearization. 7. - 9. Finite volume method for the incompressible Navier-Stokes equations on unstructured grids in cell-centered approach (approximate solution, discretization of the volume integral, convective, diffusive and source terms, numerical diffusion, explicit and implicit time discretization schemes, nonlinearity of the N-S equations, pressure-velocity coupling) 10. Methods and approaches in CFD (overview of the numerical methods in CFD, CFD workflow) 11. Mathematical models in CFD (single- / multiphase flow, newtonian / non-newtonian fluids, incompresible / compressible flow, viscous / inviscid vlow, steady / unsteady flow, laminar / turbulent flow, turbulence modeling, boundary conditions) 12. Computational grids (terminology, structured, unstructured and block-structured meshes, mesh quality, general recommendations for grid generation, examples of computational meshes, mesh generators in OpenFOAM) 13. - 14. Linear system solvers and parallelization in CFD (pressure and density-based solvers, segregated and monolithic solvers, structure of the linear systems in CFD, direct and iterative methods, properties of the classical iterative methods, multigrid methods, convergence, residual, parallelization, hardware architectures for parallel CFD, OpenMP and MPI) Seminars: 1. Mathematical formulation of flow and transport problems. Analytical solutions. 2. Numerical solution of contaminant transport in 2D by finite volume method. 3. Finite volume method for contaminant transport with diffusion. 4. Solution of potential flow and heat transport using finite element method. 5. Finite element method for Stokes problem. 6. Finite element method for Navier-Stokes equations. Picard and Newton method for linearization. 7. Numerical solution of coupled flow and transport. 8. Role of CFD in industry and research. Introduction of OpenFOAM (open-source CFD package). Lid-driven cavity flow. 9. Finite volume method in OpenFOAM (preprocessor, solver, postprocessor). Laminar pipe flow. 10. Finite volume method (accuracy vs. stability, convergence). Channel flow in low Re. 11. Turbulence modeling (length and time scales in turbulent flows, RANS). Turbulent flow in a 2D channel. 12. Turbulence modeling (near-wall modeling, wall functions). Flow over a backward-facing step. 13. Aerodynamic forces and coefficients. External bluff body flow. 14. Topic according to current interest. CFD project submission.
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
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H.K. Versteeg, W. Malalasekera. An introduction to Computational Fluid Dynamics. Prentice Hall, 2007. ISBN 978-3-319-99693-6.
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J.H. Ferziger, M. Perić. Computational methods for fluid dynamics. Berlin, 2002. ISBN 978-3-642-56026-2.
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M. Feistauer, J. Felcman, I. Straškraba. Mathematical and computational methods for compressible flow. Oxford University Press, 2003. ISBN 0198505884.
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M. Kozubková. Modelování proudění tekutin Fluent. VŠB-TU Ostrava, 2008.
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