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FSG3114 Numerical Methods in Fluid Mechanics 7.5 credits

An in-depth course on numerical methods for computer simulation of fluid flows. Together with SG2224 Applied Computational Fluid Dynamics, a comprehensive course on theory and practice of computational fluid dynamics.

About course offering

For course offering

Spring 2024 Start 16 Jan 2024 programme students

Target group

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Part of programme

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P3 (7.5 hp)


16 Jan 2024
15 Mar 2024

Pace of study


Form of study

Normal Daytime

Language of instruction


Course location

KTH Campus

Number of places

Places are not limited

Planned modular schedule


For course offering

Spring 2024 Start 16 Jan 2024 programme students

Application code



For course offering

Spring 2024 Start 16 Jan 2024 programme students


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Course coordinator

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Headings with content from the Course syllabus FSG3114 (Spring 2023–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Short introduction with a review of other numerical methods or the basic equations of fluid dynamics. Conservation laws: the Navier-Stokes equations.

Different levels of approximation, the Euler and boundary-layer equations. Basics of finite approximations for partial differential equations.

Mathematical properties of hyperbolic systems. Numerical treatment of shocks. Finite difference and volume methods. Boundary conditions. High-resolution methods. Coordinate transformation and grid-quality assessment. Practical algorithms for compressible and incompressible flow. Computer exercises with methods for the Euler equations in 1D and different approximations for 2D compressible and incompressible flows.

Intended learning outcomes

After reading this course the student should be:

  • familiar with the differential equations for flow phenomena and numerical methods for their solution
  • able to use and develop flow simulation software for the most important classes of flows in engineering and science.
  • able to critically analyse different mathematical models and computational methods for flow simulations
  • able undertake flow computations using current best practice for model and method selection, and assessment of the quality of results obtained.

Literature and preparations

Specific prerequisites

  1. 1. A course in computer science or programming (e.g. DD1337);
  2. 2. Background in either fluid dynamics or numerical methods, corresponding to one of the second level courses in numerical methods, e.g. SF2520, 2521, 2561, or a course in fluid dynamics e.g. SG2214 or equivalent.
  3. English B

Recommended prerequisites

  • A course in computer science or programming (e.g. DD1342);
  • Background in either fluid dynamics or numerical methods, corresponding to one of the second level courses in numerical methods DN2220-DN2225, DN2250-DN2260, DN2266, or a course in fluid dymamics e.g. SG2214 or equivalent.


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Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


  • LAB2 - Computer assignment, 4.5 credits, grading scale: P, F
  • TEN1 - Written exam, 3.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

One written examination with minimum performance that corresponds to grade B for the Master's course SG2212 (TEN1) 3,0 hp.

Homework and computer assignments (LAB1) 4,5 hp. Compared to the corresponding moment in SG2212 (LAB1) 4,5 hp required completion of an extra assignment.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

SG2213 Applied Computational Fluid Dynamics covers selected industrial and research topics in students projects with invited specialists.

Postgraduate course

Postgraduate courses at SCI/Mechanics