Fluid mechanics

2022/2023
Programme:
Financial Mathematics, Second cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M1
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

Kinematics of the fluid flow:
Eulerian description. Rate of deformation tensor. Material derivative and transport theorems. Stream lines, pathlines, streak lines, vortex lines.
Physical properties of fluids:
Stress vector and tensor. Mass conversation law. Momentum equation. Thermodinamical principles. Constitutive relation. Hydrostatics.
Newtonian fluids:
Viscosity. Navier-Stokes equation. Examples of laminar flow, plane Coette flow, Poiseuille flow, Stokes problem. Diffusion and convection of the vorticity. Turbulence.
Ideal fluids:
Eulerian equation. Bernoulli's theorem. Potential flow of incompressible fluid.
Complex variable methods. Compressible fluid. Acoustic approximation.
Review of numerical methods in fluid mechanics:
Equations in conservative forms. Finite volume method. Benchmark problems.

Readings

L. Škerget: Mehanika tekočin, Fakulteta za strojništvo, Ljubljana, 1994.
G.K. Batchelor, An introduction to Fluid Dynamics, Cambridge University Press, 1967.
A. J. Chorin, J. E. Marsden: A Mathematical Introduction to Fluid Mechanics, 3rd edition, Springer, New York, 2000.
J. H. Spurk: Fluid Mechanics : Problems and Solutions, Springer, Berlin, 1997.

Objectives and competences

The goal is to obtain basic knowledge of fluid mechanics. Acquired knowledge allows further individual study of fluid mechanics.

Intended learning outcomes

Knowledge and understanding:
Knowledge and understanding of basic prnciples of fluid mechanics.
Application:
Application of the acquired knowledge in solving real-life problems of fluid mechanics. First step for further graduate level study of fluid mechanics.
Reflection:
Crossbreeding of different mathematical subjects within a single course and their application in the field of fluid mechanics.
Transferable skills:
Understanding of fluid mechanics in the context of the continuum mechanics. Ability of solving related problems from the applied mathematics.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

Regular homework assignments
Oral presentation of homework

Grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

MEJAK, George. Finite element solution of a model free surface problem by the optimal shape design approach. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1997, vol. 40, str. 1525-1550. [COBISS-SI-ID 9983833]
MEJAK, George. Numerical solution of Bernoulli-type free boundary value problems by variable domain method. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1994, let. 37, št. 24, str. 4219-4245. [COBISS-SI-ID 8166745]
MEJAK, George. Finite element analysis of axisymmetric free jet impingement. International journal for numerical methods in fluids, ISSN 0271-2091, 1991, let. 13, št. 4, str. 491-505. [COBISS-SI-ID 8167769]