Subject: Mechanics of Continuous Environments	Code: MM278	

Semester	 Hours: C+S+L	Type	 Section	
1	2+1+1	compulsory	Mathematical Models in Mechanics and Astronomy	

Teaching Staff in Charge	Prof. PETRILA Titus, Ph.D., tpetrila@cs.ubbcluj.ro	
Aims	The aim of this course is to present fundamental notions of fluid mechanics regarding the motion and deformation of continuous media, in particular of fluids. The Euler and Navier-Stokes equations are also established. Another purpose of this course is to give an introduction in some special chapters of viscous fluid mechanics, with a special attention to the theory of viscous linearized flows. Further, we present the singularity method and also the theory of hydrodynamic potential. A special part of this course is concerned with boundary integral methods for Stokes flows in the presence of solid bodies and fluid particles. Finally, we give some numerical methods in order to treat numerically the proposed problems, with a special attention to the boundary element method. 
	
Content	1. Preliminaries.
-Description of the fluid flows.
-General principles of fluid flows.
-Constitutive equation of Newtonian fluid. 
-The Euler equation and the Navier-Stokes equation.
-Linearization of the equations of fluid flow. 
2. Exact solutions of the Navier-Stokes equations.
3. The Stokes linearization method 
-Properties of steady and unsteady Stokes flows
-The generalized Lorentz reciprocal identity for Stokes flows
-Uniqueness of the solution of Stokes flow
4. The singularity method.
-Green's functions of Stokes flow. Properties. 
-The fundamental solutions of Stokes flow. Applications.
5. The theory of hydrodynamic potentials.
6. Direct boundary integral representations of Stokes flow:
-The boundary integral representation of the velocity field of Stokes flow
-The boundary integral representation of the pressure field of Stokes flow
7. Indirect boundary integral representations of Stokes flows.
-The completed double-layer boundary integral equations method. 
-Applications: the study of Stokes flows past or due to the motion of solid bodies and viscous drops.
-Existence and uniqueness results
8. Numerical methods applied to certain Stokes flow problems with a special attention to the boundary element method

	
Selective References	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. KOHR, MIRELA: Studiul unor Miscari Fluide Vascoase Incompresibile prin Metode Integrale pe Frontiera. Cluj-Napoca: Presa Universitara Clujeana, 1997.
5. PETRILA, TITUS - TRIF, DAMIAN: Metode Numerice si Computationale in Dinamica Fluidelor. Cluj-Napoca: Ed. Digital Data Cluj, 2002.
6. POP, IOAN - INGHAM, DEREK B.: Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. London: Pergamon Press, 2001.
7. POZRIKIDIS, COSTAS: Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge: Cambridge University  Press, 1992.
8. POZRIKIDIS, COSTAS: Introduction to Theoretical and Computational Fluid Dynamics.  Oxford: Oxford University Press, 1997.
9. POWER, HENRY - WROBEL, LUIZ C.: Boundary Integral Methods in Fluid Mechanics. Southampton: WIT Press: Computational Mechanics Publications, 1995.
10.TRUESDELL, CLIFFORD - RAJAGOPAL, KUMBAKONAM R.: An Introduction to the Mechanics of Fluids. Basel: Birkhauser, 2000.	
Assessment	Exam (70%)+ student activity (30%).