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

Code	Subject	
MM271	Approximate (Analytical and Numerical) Methods for Fluid Dynamics	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematical Models in Mechanics and Astronomy - in English	2	2+2+0		compulsory	

Teaching Staff in Charge	Prof. PETRILA Titus, Ph.D., tpetrila@cs.ubbcluj.ro	
Aims	The course presents advanced topics in Fluid Dynamics with a special accent on analitical and numerical approximation methods. Subsonic, supersonic and transonic motions are analized through examples, and in each case several approximation methods are discussed.	
Content	1.Deformable Continuum's Equations. The case of Inviscid Fluid and the case of Viscous Fluid.

2.Numerical methods for second order Partial Differential Equations. Stability, consistence and convergence for Finite Difference Schemes. Finite Element methods.
Irrotational Flows of the Incompressible Inviscid Fluids in two Dimensional Case.

3.Conformal Mapping. Principles of the Profiles Theory.
Notions on the Hodograph Method.
Approximation method for Conformal Mapping. Panels method (Sources or Vortices) for   
Two Dimensional Flows past a profile.

4.Theory of Thin Airfoils.

5.The Steady Irrotational Flows produced by the Motion of an Obstacle in an Ideal Fluid.

6.Boundary Element Methods and CVBEM applied in profile theory.

7.Barotrop Compressible Fluid Flows. Stechen's equations. Analytical methods for the approximation of the corresponding nonlinear system.

8.Theory of Linearization's principle. The Glauert-Prandtl' rule and Ackeret' rule.

9.Finite Difference schemes. Diffusion Equation.
Viscous incompressible fluids flow. Adimensional variables. 

10.Burgers' equations, Analytical solution, solving the nonlinearity through adequate finite difference schemes.

11.Flows with large Reynolds numbers. Boundary Layer equation.

12.Flows with small Reynolds numbers. Stokes system.

13.Numerical methods based on Integral equations.

14.Navier-Stokes equations. Approach with the finite element method.

Bibliography	1.  TITUS PETRILA, DAMIAN TRIF, Metode numerice si computationale in mecanica fluidelor, Edit. Digital Data, Cluj-Napoca, 2002
2.  TITUS PETRILA, CALIN GHEORGHIU Metode element finit si aplicatii, Editura Academiei Române, 1987
3.  CAIUS IACOB, Introduction mathematique a la mecanique des fluides. editura Academiei Române si Editions Gauthier-Villars, 1959.
4.  LAZAR DRAGOS, Principiile mecanicii mediilor continue, Editura Tehnica, Bucuresti, 1981
5.  DANIEL EUVRARD, Resolution numerique des equations aux derivees partielles, editions Masson, Paris, 1994
6.  CHUEN YEN CHOW, An Introduction to Computational Fluid Dynamics, John Wiley & Sons, NY, 1980
7.  D. J. ACHESON, Elementary Fluid Dynamics, Clarendon Press, 1992
8.  H. DUMONTET, GEORGES DUVAUT,ETC Exercices de mecanique des millieux continus, Editions Masson, Paris, 1994
9.  TITUS PETRILA, Lectii de mecanica mediilor continue, lito UBB, 1980
10.  PAUL GERMAIN, Mecanique des millieux continus, Editions Masson, Paris, 1962
11. TITUS PETRILA, DAMIAN TRIF, Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics, Springer USA, 2005

	
Assessment	Exam.