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.
Fluid mechanics
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.
The goal is to obtain basic knowledge of fluid mechanics. Acquired knowledge allows further individual study of fluid mechanics.
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.
Lectures, exercises, homeworks, consultations
2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
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]
