Numerical Analysis: Numerical Simulations of Flow Problems

This course introduces modern numerical methods for solving nonlinear conservation laws, with a focus on fluid mechanics. You will learn how simulations are used to model gas dynamics and flow phenomena, and how mathematical challenges like shock waves and discontinuities are handled in practice.

Topics covered include

• Computational fluid dynamics models
• Hyperbolic conservation laws (weak solutions, entropy solutions, shock waves)
• Discontinuous Galerkin methods
• Gas dynamics simulations
• Krylov subspace methods with preconditioning
• Jacobian-free Newton-Krylov methods
• Multigrid methods for flow problems

NUMN28 is an alternativecompulsory course within the Master’s Programme in Mathematics with a specialization in Numerical Analysis at Lund University. It is also available as an elective course for students in mathematics Bachelor’s programmes and as a standalone course.

The course combines lectures with practical assignments and a final project. While the assignments are optional, they prepare you for the mandatory project, which includes a written report and an oral examination.

You will work hands-on with advanced numerical techniques, implement algorithms, and analyse simulation results. The course encourages independent problem-solving and integrates knowledge across topics.

Assessment is based on a written project report (graded Fail/Pass) and an oral examination (graded Fail/Pass/Pass with Distinction). To pass the course, you must complete both components. To pass with distinction requires a good ability to critically and systematically integrate knowledge from the various parts of the course, and to handle, analyse and assess the questions posed in the project and the oral examination.

After completing this course, you will be prepared to work with advanced simulations in both academic and industrial environments. Your skills will be relevant in areas such as aerospace and windturbine design, climatesystem modelling, scientific computing, and applied mathematics. The course also provides a solid foundation for continued studies in numerical analysis, scientific computing, and related disciplines, giving you experience in solving complex computational problems—competencies that are in high demand across research and technology sectors.

Prerequisites

For admission to the course English 6/B and at least 30 credits mathematics and additional 60 credits in mathematics and/or physics are required, including knowledge corresponding to the courses NUMN32 Numerical Methods for Differential Equations, 7.5 credits.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 21,250
First payment: SEK 21,250

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.