Mathematical Models and Numerical Methods for Fluid Mechanics
The participants of the course will read and present chosen articles and book extracts in the scientific area. The course is planned in four stages as described below, and the papers are grouped accordingly. Five course meetings will be scheduled. At the first one, an overview will be given of the chosen literature, and at the remaining occasions, papers of the consecutive course stages will be presented by the participants. There will be one course meeting every four weeks, and the dates will be decided at the course start. The course is given at graduate level and corresponds to 6 hp.
Course start
Thursday, 15 January 2015, 13:15-15:00, room 2415b.
Teacher
Course stages
1. Formulation of mathematical models of fluid mechanics. One-phase flow will be considered, taking compressibility effects and viscosity into account with the simplest constitutive relations. Eulerian and Lagrangian description of the motion of a continuum. Three different formulations of the governing equations, in the form of (i) A partial differential equation; (ii) A variational formulation; or (iii) A conservation law for an arbitrary fluid element.
2. Numerical solution approaches for the equations for conservation of mass and momentum by: (i) The finite difference method; (ii) The finite volume method; (iii) The Galerkin method. For the last approach we will consider (iiiA) The spectral method and (iiiB) The finite element method.
3. A complete solution method (of the finite volume type) for the incompressible Navier-Stokes equations. Consideration of boundary and initial conditions as well as the special coupling of the velocity and pressure fields in the case of incompressibility.
4. Miscellaneous additional topics: Mesh generation, introduction to turbulence modelling and practical validation/benchmark problems. PhD project algorithms.
Schedule:
| date&time | room | topic | |
|---|---|---|---|
| 1 | January 15, 13-15 | 2415b | Course start |
| 2 | February 5, 13-15 | 2415b | Mathematical models of fluid mechanics |
| 3 | March 5, 13-15 | 2415b | Numerical solution approaches |
| 4 | April 9, 13-15 | 2415b | A complete solution method |
| 5 | May 7, 13-15 | 2415b | Miscellaneous additional topics |