Course: Introduction to Mathematical Modelling

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Course title Introduction to Mathematical Modelling
Course code KI/UMM
Organizational form of instruction Lecture + Seminary
Level of course unspecified
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course unspecified
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
Course content
Basic eqations of fluid dynamics: description of the flow, transport theorem, continuity equation, equations of motion, stress tensor, Euler and Navier-Stokes equations, energy equation, thermodynamical relations. Mathematical theory of compressible flow: Euler equations, properties of the Euler equations, Cauchy problem, boundary conditions, weak solution. Finite volume method: Finite volume mesh, derivation of the finite volume scheme, properties of the numerical flux, construction of the numerical flux, Godunov method, Riemann solver.

Learning activities and teaching methods
unspecified
Learning outcomes
Introduction to the mathematical modelling. The emphasis is put on the active learning of basic mathematical and physical concepts. Formulation of conservation laws in the form of the differential equations, constitutive and rheological relations, Euler equations, finite volume method, Riemann solver, numerical flux, adaptive methods, higher order methods.

Prerequisites
unspecified

Assessment methods and criteria
unspecified
Recommended literature
  • Feistauer M., Felcman J., Straškraba I. Mathematical and Computational Methods for Compressible Flow, Oxford University Press, Oxford. 2003.
  • Feistauer M. Mathematical Methods in Fluid Dynamics. Longman Scientific-Technical, Harlow, l993.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester