Course detail
Mathematical Methods in Fluid Dynamics
FSI-SMMAcad. year: 2020/2021
Basic physical laws of continuum mechanics: laws of conservation of mass, momentum and energy. Theoretical study of hyperbolic equations, particularly of Euler equations that describe the motion of inviscid compressible fluids. Numerical modelling based on the finite volume method and discontinuous Galerkin method. Discontinuous Galerkin method for viscous compressible flows. Numerical modelling of viscous incompressible flows: pressure-correction method SIMPLE and finite element method.
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Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
FORM OF EXAMINATIONS: The exam is oral. As a result of the exam students will obtain 0--70 points.
FINAL ASSESSMENT: The final point course classicifation is the sum of points obtained from both the practisals (0--30) and the exam (0--70).
FINAL COURSE CLASSIFICATION: A (excellent): 100--90, B (very good): 89--80, C (good): 79--70, D (satisfactory): 69--60, E (sufficient): 59--50, F (failed): 49--0.
If we measure the exam success in percentage points, then the classification grades are: A (excellent): 100--90, B (very good): 89--80, C (good): 79--70, D (satisfactory): 69--60, E (sufficient): 59--50, F (failed): 49--0.
Course curriculum
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Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
J.H. Ferziger, M. Peric: Computational Methods for Fluid Dynamics, Springer-Verlag, New York, 2002. (EN)
K. H. Versteeg, W. Malalasekera: An Introduction to Computational Fluid Dynamics, Pearson Prentice Hall, Harlow, 2007. (EN)
M. Feistauer, J. Felcman, I. Straškraba: Mathematical and Computational Methods for Compressible Flow, Oxford University Press, Oxford, 2003 (EN)
V. Dolejší, M. Feistauer: Discontinuous Galerkin Method, Springer, Heidelberg, 2016. (EN)
Recommended reading
Elearning
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Lecture
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Syllabus
2. Constitutive relations, thermodynamic state equations, Navier-Stokes and Euler equations, initial and boundary conditions.
3. Traffic flow equation, acoustic equations, shallow water equations.
4. Hyperbolic system, classical and week solution, discontinuities.
5. The Riemann problem in linear and nonlinear case, wave types.
6. Finite volume method, numerical flux, local error, stability, convergence.
7. The Godunov's method, flux vector splitting methods: Vijayasundaram, Steger-Warming, Van Leer, Roe.
8. Boundary conditions, secon order methods.
9. Discontinuous Galerkin method for compressible inviscid flow: introduction to DGM, discretization of 2D Euler equations.
10. Discontinuous Galerkin method for compressible inviscid flow: elementary matrices and vectors, assembly process, time discretization.
11. Discontinuous Galerkin method for 2D compressible viscous flow.
12. Finite volume method for viscous incompressible flows: the SIMPLE algorithm on rectangular mesh.
13. Finite volume method for viscous incompressible flows: the SIMPLE algorithm for unstructured mesh.
Computer-assisted exercise
Teacher / Lecturer
Syllabus
Elearning