SG3114 Numerical Methods in Fluid Mechanics 7.5 credits

Numeriska metoder i strömningsmekanik

An in-depth course on numerical methods for computer simulation of fluid flows. Together with SG2213 Applied Computational Fluid Dynamics, a comprehensive course on theory and practice of computational fluid dynamics.

  • Education cycle

    Third cycle
  • Main field of study

  • Grading scale

Information for research students about course offerings

The course is given in parallel with SG2212 in period 3.

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.

Course main content

Short introduction with review of other numerical methods or the basic equations of fluid dynamics (the class will be divided in two groups). Conservation laws: the Navier-Stokes equations. Different levels of approximation, the Euler and Reynolds Averaged equations. Turbulence models. Basics of finite approximations for partial differential equations. Mathematical properties of hyperbolic systems. Numerical treatment of shocks. Finite volume and finite element methods. Boundary conditions. High-resolution methods. Grid generation. 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.

Eligibility

A course in computer science or programming (e.g. DD1342);
2. 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 dynamics e.g. SG2214 or equivalent.

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.

Literature

To be announced at course start. In 08/09: Numerical Computation of Internal & External Flows, Charles Hirsh, Butterworth-Heineman, Second Edition, ISBN: 978-0-7506-6594-0, was used.

Examination

Requirements for final grade

One written examination with minimum performance that corresponds to grade B for the Master's course SG2212 (TEN1).
Homework and computer assignments for the master’s course SG2212 (LAB1). Additional specific project part for SG3114.

Offered by

SCI/Mechanics

Contact

Philipp Schlatter

Examiner

Philipp Schlatter <philipps@kth.se>

Add-on studies

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

Version

Course syllabus valid from: Spring 2016.