Checking date: 22/04/2018

Course: 2019/2020

Fluid mechanics and partial differential equations
Study: European Master in Nuclear Fusion Science and Engineering Physic (273)

Coordinating teacher:

Department assigned to the subject: Department of Physics

Type: Electives
ECTS Credits: 3.0 ECTS


Students are expected to have completed
Basic knowledge of mechanics (graduate level) and differential equations.
Competences and skills that will be acquired and learning results.
The course intends to provide with the basics for an understanding of the fluid mechanics theory making emphasis on mathematical aspects such as modelling, mathematical analysis of the models, stability and so on. Different techniques of partial differential equations will be introduced. The magnetically confined plasma will be considered in the framework of the ideal MHD. The course will provide the student with an appropiate training in simple fluid mechanics problems and its mathematical treatment.
Description of contents: programme
1. Basic Modelling: conservation laws and constitutive equations. 2. Elliptic problems. Movements to low Reynolds numbers. Stokes flows 3. Parabolic problems. Existence and uniqueness of solutions. Movements to low Reynolds numbers. Porous media and lubrication 4. Hyperbolic problems. Movements to high Reynolds numbers. Euler equations. Acoustics 5. Asymptotic techniques. Boundary layers 6. Stability and chaos. Applications in hydrodynamics 7. The ideal MHD and Grad-Safranov
Learning activities and methodology
* Teaching Methods: Classroom lectures and classroom problem solving sessions. * Course Material: Copies of the presentations.
Assessment System
  • % end-of-term-examination 50
  • % of continuous assessment (assigments, laboratory, practicals...) 50
Basic Bibliography
  • Acheson, D.J.. Elementary Fluid Dynamics. Clarendon Press, Oxford. 1990
  • Temam, R.. Navier-Stokes Equations. North-Holland, Amsterdam. 1984
  • Temam, R. and Miranville, A.. Mathematical Modeling in Continuum Mechanics. Cambridge Univ. Press. 2001
Additional Bibliography
  • Evans, L.C.,. Partial Differential Equations. AMS, Providence. 1998
  • Sherman, F. S.. Viscousflows. McGraw-Hill, New York. 1990
  • Whitham, G.. Linear and Nonlinear Waves. Wiley, New York. 1974

The course syllabus and the academic weekly planning may change due academic events or other reasons.