Entry requirements

120 credits in science/engineering. Scientific Computing for Partial Differential Equations. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student shall be able to:

• Explain and distinguish the types of partial differential equations (PDEs) used in science and engineering
• Account for the most important PDEs that model fluid mechanics
• Learn different numerical methods, such as finite elements (and possibly finite differences or discontinuous Galerkin methods), to discretize the fluid equations
• Analyze the stability, consistency and convergence of these numerical methods
• Write code in Matlab/Python to solve problems in 1D and 2D
• Use the open source library FEniCS Project to solve more advanced problems in 2D and 3D

Content

Solutions to computational problems in fluid dynamics that arise in engineering applications, such as subsonic and supersonic flows, shock-capturing methods, and numerical regularizations. Scalar nonlinear conservation laws and their practical difficulties from both an analytical and implementation point of view.. Handling of these problems using numerical these problems using numerical methods, ensuring that stability and consistency of numerical approximations are preserved. The second part of the course deals with systems of compressible Euler equations.

Programming in either Matlab or Python. The FEniCS project has a Python interface.

Instruction

Lectures, problen solving sessions, laboratory exercises

Assessment

Written exam (3 credits), oral and written presentation of assignments and project work (2 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.