Hydrodynamics
Code
9583
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Engenharia Civil
Credits
6.0
Teacher in charge
Luís Miguel Chagas da Costa Gil
Teaching language
Português
Objectives
To give students advanced knowledge in the areas of conservation laws, the physical meaning of its terms, its application to free-surface flows and possible simplifications and consequent limitations. At the end of the curricular unit students should be able to, autonomously, develop research and apply concepts in the area of hydrodynamics. Thus, students should have the following abilities:
• Expertise in the physics of conservation laws.
• Comprehension of particular solutions of the conservation laws.
• Comprehension of the role of pressure and passive scalars.
• Expertise in the physics of Reynolds equations.
• Comprehension of the vorticity equations.
• Expertise in the application of shallow water equations.
Subject matter
1. Continuity equation. Momentum equations (Navier-Stokes equations).
2. Particular solutions.
3. Potential flows.
4. The role of pressure.
5. Passive scalars.
6. Reynolds equations (time average). Reynolds stresses.
7. Vorticity equations.
8. Shallow water equations (dynamic wave, kinematic wave, no inertial wave, gravity wave, quasi steady dynamic wave).
Bibliography
G.K. Batchelor. An Introduction to Hydrodynamics. Cambridge University Press, 1967.
C.R. Doering and J.D. Gibbon. Applied Analysis of the Navier-Stokes Equations. Cambridge Texts in Applied Mathematics, 1995.
P.G. Lemarie-Rieusset. Recent Developments in the Navier-Stokes Problem. Research Notes in Mathematics, 431, Kluwer Academic Publishers, 2002.
L. Stupelis. Navier stokes equations in irregular domains. Mathematics and its applications 326, Kluwer Academic Publishers, 1995.
J.-M. Hervouet. Hydrodynamics of Free Surface Flows: Modelling with the Finite Element Method. John Wiley & Sons, 2007.