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Lecturer(s)
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Stebel Jan, doc. Mgr. Ph.D.
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Šidlof Petr, doc. Ing. Ph.D.
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Course content
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Lectures: 1. Introduction. Basic types of problems in CFD. 2. Finite volume method (FVM) for linear transport equation. Solution by explicit time discretization, stability. 3. Finite difference method for linear convection-diffusion equation. Explicit/implicit time discretization. 4. Finite element method (FEM) for linear convection-diffusion equation. Stabilization, discontinuous Galerkin method. 5. Introduction into CFD. Governing equations for the fluid flow. Boundary conditions. 6. Space discretization. Classification of the numerical methods in CFD. 7. Computational grid, types and properties. Mesh quality, mesh refinement. 8. Time discretization, linearization. 9. Solution of the linear systems. 10. Postprocessing and validation. 11. FVM for hyperbolic conservation laws. 12. Application of FVM to inviscid fluid flow models, shallow water equations, wave equation. 13. FEM for flow of viscous incompressible fluid. 14. Operator splitting method for coupled problems (transport and chemical processes, flow and heat transfer). Tutorials: 1. Review. Green's theorem, weak formulation of linear convection-diffusion equation, Galerkin's method. 2. Finite volume method (FVM) for linear transport equation in 1D. Solution by explicit time discretization, stability and numerical diffusion. 3. Finite difference method for linear convection-diffusion equation in 2D. Explicit/implicit time discretization. 4. Finite element method (FEM) for linear convection-diffusion equation. Stabilization, discontinuous Galerkin metod. 5.-7. CFD simulation of stationary laminar flow in a cavity. 8.-10. CFD simulation of flow past a circular cylinder at different Reynolds numbers (laminar flow, simulation with a turbulence model) 11. Hyperbolic conservation laws - transformation to canonical form, derivation of FVM, assembly of systém matrix for Burgers' equation. 12. Application of FVM to models of inviscid fluids, shallow water equations, wave equation. 13. FEM for flow of viscous incompressible fluid. Choice of finite elements, matrix assembly. 14. Operator splitting method for coupled problems (transport and chemical processes, flow and heat transfer).
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
- Class attendance
- 56 hours per semester
- Home preparation for classes
- 27 hours per semester
- Preparation for exam
- 54 hours per semester
- Preparation for credit
- 12 hours per semester
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Learning outcomes
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The course presents an introduction to the computational fluid dynamics (CFD). Students will learn basic numerical methods for the solution of flow and transport problems, general scheme of solution of practical CFD problems as well as its realization in a specific CFD software. After attending the lectures and tutorials, the studens is able to build a suitable model for the solution of simple flow and transport problems and solve it in some of the available computational environments.
The student will obtain basic overview of problems in fluid mechanics and methods of their solution. They will be able to derive and implement simple numerical schemes and solve simple problems in a CFD software.
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Prerequisites
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Basic knowledge of principles of fluid mechanics is expected.
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Assessment methods and criteria
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Combined examination
To obtain a credit the student has to realize and hand in specific assignments. Examination is in written and oral form.
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Recommended literature
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H.K. Versteeg, W. Malalasekera. An introduction to Computational Fluid Dynamics. Prentice Hall, 2007.
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J.H. Ferziger, M. Perić. Computational methods for fluid dynamics.
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M. Feistauer, J. Felcman, I. Straškraba. Mathematical and computational methods for compressible flow. Oxford University Press, 2003.
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M. Kozubková. Modelování proudění tekutin Fluent. VŠB-TU Ostrava, 2008.
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