MA8502 - Numerical solution of PDEs - Fall 2014

Onsdag 20nde: I mangel på et permament hjem så vil forelesingen bli holdt på lunsjrommet i 13nde etasje. Tidspunkt er som avtalt 10:15 - 12:00.

Important: There will be an organisational meeting where we determine time and place for lectures. If you intend to follow the course, you are strongly advised to show up for this meeting. The meeting is at room 734 at 12:15 on Tuesday 19th of August.

Lectures are held

• Tuesdays: 10:15-12:00 in R90 (Realfag)
• Wednesdays: 14:15-16:00 in K25 (Chemistry)

The exam will be held at S21 in SBII on Friday 5.12 and Monday 8.12.

• Schedule

The syllabus will be based on various handouts that will be made available as the course progress.

• Lecture Notes by Ismail Celik (Chapters 1-8 and 11, the specific models in Chapter 6 are not relevant)

• Numerical methods for NS (Langtangen, Mardal, Winther)

• Stationary Stokes (Rønqvist)
• Saddlepoint problems 1 (Rønqvist)
• Saddlepoint problems 2 (Rønqvist)

• Approximation and interpolation by higher order polynomials (E. Rønqvist)
• Interpolation basics (Doron Levy - UMD)

• Spectral discretization in 1D (E. Rønqvist)
• Spectral discretization in 2D, 3D (Rønqvist)
• Deformed geometries (Rønqvist)
• Deformed geometries 2 (Rønqvist)

• Mixed conditions along curved boundaries (Rønqvist)

• Ulrik's notes

• Derivation of governing equations (from PhD thesis)
• Mathematical principles of classical fluid mechanics (derivation of equations only) (J. Serrin)

30% of the final grade will be based on the evaluation of a project.

• Project description: project.pdf
• The grids: http://turbmodels.larc.nasa.gov/naca0012_grids.html
• The original challenge: http://turbmodels.larc.nasa.gov/naca0012_val.html

Here I will post code to help you along with the project. The code will be Matlab and C++ only.

• readgrid.m (Matlab)
• plotgrid.m (Matlab)

• Grid help (load grid from file and see it)

The following is a tentative lecture plan that may change as the semester progress.

Week 34: Introduction. Why higher order. Interpolation. Representation in finite dimensions. The equations of fluid mechanics.

Week 35: Convection-Diffusion equations. On the balance of convection and diffusion. Stability vs. Accuracy.

Week 36: Laplace equation: Finite elements of arbitrary order. Spectral methods in one dimension.

Week 37: Laplace equation: Spectral methods in several dimensions.

Week 38: Laplace equation: Spectral methods on deformed geometries.

Week 39: Convection equation: Finite volume methods. Upwinding. Finite element methods. Streamline diffusion.

Week 40: Convection equation: Discontinuous Galerkin methods. Transport and spectral methods.

Week 41: The steady Stokes problem. Divergence contraint. Spectral discretization.

Week 42: Week set of for project work.

Week 43: Week set of for project work.

Week 44: Operator splitting

Week 45: Introduction to Turbulence modeling.

Week 46: Review

Week 47: Review

The course will be given by Trygve Karper. He may be found at office 1342.