Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MMM1004	Approximative Methods in Fluid Mechanics	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	3	2+2+0	speciality	optional	

Teaching Staff in Charge	Lect. GROSAN Teodor, Ph.D., tgrosan@math.ubbcluj.ro	
Aims	Advanced topic in fluid flow is presented, specially analytical and numerical methods. Inviscid fluid flow is modelled using complex variable functions; viscous fluid flow is modelled using boundary layer approximation. Numerical algorithms using finite differences and finite volumes discretization are presented.	
Content	1. Continuum media equations. Inviscid and viscous fluid cases.

2. 2D potential flow of inviscid incompressible fluids.

3. Conformal mapping method. Principles of profiles theory.

4. Thin wing theory.

5. Compressible fluid flow. Steichen equations. Analytical methods for the non-linear system approximation.

6. Finite difference schemes. (explicit and implicit). Diffusion equation.

7. Incompressible viscous fluid flow. Dimensionless variables.

8. Large  Reynolds number case. Boundary layer equations.

9. Small Reynolds number case. Stokes&#8217; system..

10. Finite volume method.
	
Bibliography	1. DRAGOS, LAZAR: Mecanica Fluidelor. Bucuresti: Editura Academiei, 1999.
2. KOHR, MIRELA - POP, IOAN: Viscous Incompressible Flow for Low Reynolds Numbers. Southampton-Boston: WIT Press (Wessex Institute of Technology Press): Computational  Mechanics Publications, 2004.
3. KOHR, MIRELA: Probleme Moderne ale Mecanicii Fluidelor Vascoase. Cluj-Napoca: Presa Universitara Clujeana, 2000.
4. PETRILA, TITUS - TRIF, DAMIAN: Metode Numerice si Computationale in Dinamica Fluidelor. Cluj-Napoca: Ed. Digital Data Cluj, 2002.
5. Lai, W.M., Rubin, D., Krempel, E.: Introduction to Continuum Mechanics, Elsevier, 1999.
6.Patankar S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere, 1980
7. BRADEANU, PETRE: Mecanica fluidelor, Ed. Tehnica, Bucuresti, 1973.

Assessment	Final mark is given by:
Written exam:  75%
Seminar activity: 25%