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Course, academic year 2017/2018
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Introduction to Mathematical Modelling - NMNM334
Czech title: Úvod do matematického modelování
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:3/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Jiří Felcman, CSc.
prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c.
Class: M Bc. OM
M Bc. OM > Zaměření NUMMOD
M Bc. OM > Povinně volitelné
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Interchangeability : {Mathematical Modelling in Physics 1 and 2}
Incompatibility : NMOD204
Is pre-requisite for: NMNM349
Annotation -
Last update: G_M (16.05.2012)

The course is devoted to derivations of equations describing complex technical and physical structures and processes. Recommended for bachelor's program in General Mathematics, specialization Mathematical Modelling and Numerical Analysis.
Literature - Czech
Last update: G_M (16.05.2012)

Feistauer M.: Mathematical Methods in Fluid Dynamics, Longman Scientific-Technical, Harlow, 1993

Nečas J., Hlaváček I.: Úvod do mat. teorie pružných a pružně plastických těles, SNTL, Praha, 1983

Syllabus -
Last update: prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c. (08.04.2015)

Derivation of equations describing the flow:

Basic concepts of gas dynamics, description of the flow, the transport theorem, fundamental physical laws (the law of conservation of mass, the law of conservation of momentum and the law of conservation of energy) and their formulation in the form of differential equations, constitutive and rheological relations, the Euler and Navier-Stokes equations, thermodynamical laws.

Formulation of boundary value problems of the theory of elasticity:

The stress tensor, the equations for the equilibrium state, the finite strain tensor, the small strain tensor, generalized Hooke's law, the Lame equations, the Beltrami-Michell equations, basic boundary value problems of elasticity.

Modelling of inviscid flow:

Inviscid irrotational flow described by the velocity potential, existence of potential, Bernoulli equation, full potential equation, boundary conditions, flow around an airfoil, force acting on the airfoil.

Modelling of porous media flow:

Conservation of mass in flow with sources, Darcy law, permeability, equation for pressure, formulation of porous media flow with discontinuous permeability, weak formulation of elliptic equations with discontinuous coefficients.

Transport proceses:

Equation describing the transport of alloys in flow, convection-diffusion processes, applications in ekology.

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