Mathematical Methods in Fluid Dynamics 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The contents of the course is the introduction to mathematical methods in fluid dynamice. Concretely: mathematical modelling of fundamentals physical laws by means of partial differential equations, formulation of associated boundary or initial-boundary value problems for various type sof fluids as well as various type sof flows, properties and some speciál solutions of these problems.

Requirements:

Basic courses of calculus and differential equations (in the extent of the courses 01DIFR, 01MA1, 01MAA2-4, 01RMF held at the FNPE

CTU in Prague).

Syllabus of lectures:

1. Kinematice of fluids - the rate of deformation tensor, Reynolds? transport formula, compressible or incompressible flow, respectively fluid. 2. Volume and surface forces in the fluid, stress tensor. 3. Stokesian fluid and its special cases: ideal and Newtonian fluid. 4. Basic conservation laws (of mass, momentum, energy) and their mathematical modeling (equation of continuity, Euler and Navier-Stokes equations, equation of energy). 5. Second law of thermodynamics and Clausius-Duhem inequality. 6. Examples of simple solutions of the Navier-Stokes equations. 7. Laws of similarity. 8. Turbulent flows. 9. Boundary layer. 10. Basic qualitative properties of the Navier-Stokes equations - strong and weak solutions, questions of existence and uniqueness in steady and non-steady case.

Syllabus of tutorials:

Study Objective:

To learn basic principles of mathematical modelling in fluid dynamics, to learn and understand mathematical models of various type sof flows (compressible or incompressible, viscous or non-viscous, laminar or turbulent, etc.), to learn about basic methods and results in the field of qualitative properties of the Navier-Stokes equations.

Study materials:

Key references:

[1] J.Neustupa: Lecture notes on mathematical fluid mechanics.

Recommended references:

[2] G.K.Batchelor: An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge 1967.

[3] G.Gallavotti: Foundations of Fluid Mechanics, Springer 2002.

[4] W.M.Lai, D.Rubin and E.Krempl: Introduction to Continuum Mechanics. Pergamon Press, Oxford 1978.

[5] L.D.Landau and E.M.Lifschitz: Fluid Mechanics. Pergamon Press, Oxford 1959.

[6] Y.Nakayama and R.F.Boucher: Introduction fo Fluid Mechanics. Elsevier 2000.

[7] W.Noll: The Foundations of Classical Mechanics in the Light of Recent Advances in Continuum Mechanics, The Axiomatic Method. North Holland, Amstedram 1959.

[8] J. Serrin: Mathematical Principles of Classical Fluid Mechanics. In Handbuch der Physik VIII/1, ed.~C.~Truesdell and S.~Flugge, Springer, Berlin 1959.

[9] R.Temam and A.Miranville: Mathematical Modelling in Continuum Mechanics. Cambridge University Press, Cambridge 2001.

[10] G.Truesdell and K.R.Rajagopal: An Introduction to the Mechanics of Fluids. Birkhauser 2000.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (elective course)