Course detail
Mathematical Methods in Fluid Dynamics
FSI-SMMAcad. year: 2021/2022
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.
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Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
EXAM: The exam is oral. The students can obtain up to 70 points from the exam.
FINAL ASSESSMENT: The final classicifation is based on the sum of the points obtained from both the seminars and exam.
CLASSIFICATION SCALE: 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
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Syllabus
2. Law of conservation of energy, constitutive relations, thermodynamic state equations.
3. Navier-Stokes and Euler equations, initial and boundary conditions.
4. Traffic flow equation, acoustic equations, shallow water equations.
5. Hyperbolic system, classical and week solution, discontinuities.
6. The Riemann problem in linear and nonlinear case, wave types.
7. Finite volume method, numerical flux, local error, stability, convergence.
8. The Godunov's method.
9. Flux vector splitting methods: Vijayasundaram, Steger-Warming, Van Leer, Roe.
10. Boundary conditions, secon order methods.
11. Discontinuous Galerkin method for compressible inviscid flow: introduction to DGM, discretization of 2D Euler equations.
12. Finite volume method for viscous incompressible flows: the SIMPLE algorithm on a rectangular mesh.
13. Finite volume method for viscous incompressible flows: the SIMPLE algorithm for an unstructured mesh.
Computer-assisted exercise
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Syllabus