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Scientific Computing with Applications in Tribology 7.5 credits

Numeriska beräkningsmetoder med tillämpningar inom Tribologi
Second cycle, M7033T
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
Second cycle
Grade scale
G U 3 4 5
Machine Elements
Subject group (SCB)
Mechanical Engineering

Entry requirements

Foundation level courses in Mathematics (30 ECTS) Physics (22,5 ECTS) Mechanics (7,5 ECTS) and Fluid Mechanics (7,5 ECTS). It is not a prerequisite to have taken the course C0004M Programming Tools for Numerical Calculations, neither C7005M Numerics for optimisation and PDE. Prior experience of programming in MATLAB is not a requirement but facilitates course work.

More information about English language requirements


The selection is based on 20-285 credits

Course Aim

Divided into 3 categories below, you as a student should after completing the course: 

1. Knowledge and Understanding 

  • Know about some selected state-of-the-art models and simulation methods in contact mechanics, lubrication theory and wear problems, including the main concepts and underlying assumptions.
  • Understand the concept of the linear complementarity problem (LCP) and the possible application to contact mechanics.
  • Understand the concept of fast Fourier techniques (FFT) and the application to solve the elastic deformation problem.
  • Understand the concept of the finite difference method (FDM) and how it can be used for example to solve partial differential equations describing thin film flow problems.
  • Understand the concepts of verification and validation in the context of scientific computations.
  • Understand the advantage of a dimensionless model formulation for subsequent numerical analysis.

2. Skills and Abilities 

  • Be able to programme numerical solution methods in a structured and conceivable way facilitating simulations of physical processes, particularly in tribology.
  • Be able to apply the LCP formulation to solve the contact mechanics problem.
  • Be able to apply the FFT to accelerate the numerical calculation of integral equations, particularly the one describing the elastic deformation problem in contact mechanics.
  • Be able to apply the FDM to solve partial differential equations, particularly the Reynolds equation governing the pressure build-up in the thin film flow problem in a thrust bearing.
  • Be able to discretize Archard’s wear equation and solve it numerically.
  • Be able to verify numerical methods and to validate mathematical models.
  • Be able to utilize the models and simulation methods to carry out parameter studies.
  • Have developed your abilities in writing technical reports in English and your skills in oral presentation in English.
  • Be able to present the obtained results in a clear and comprehensible manner to other engineers.

3. Judgement and Assessment Ability 

  • Be able to assess accuracy and precision of the implemented simulation methods.
  • Be able to assess and judge the relevance of the results obtained with the help of models and numerical simulation methods.
  • Be able to adapt new models suitable to study related problems, with application in Tribology and in other fields.
  • Use common models and simulation methods to facilitate the development of machine elements and other applications exhibiting tribological contacts.


Contact mechanics

  • The complementarity problem (Either Contact <=> No gap or Gap <=> No contact)
  • Modelling elastic deformation
  • Discretization of integral equations (Elastic deformation problem)
  • Linear complementary problem (LCP) formulation of the contact mechanics problem
  • Fast Fourier Techniques (FFT) for calculation of derivatives and integrals

Lubrication theory

  • The thin film approximation (N-S => Reynolds equation)
  • Finite difference method (FDM) for Poisson’s type of PDE, in particular Reynold’s equation
  • Simulation of flows in bearings by means of the Reynolds equation
  • Predicting load carrying capacity (LCC) and minimum film thickness by means of fixed point iteration techniques

Modelling and simulation of wear

  • Boundary lubrication
  • Archard’s wear equation
  • Numerical solution procedure for abrasive/adhesive wear

Multiphysics modelling

  • COMSOL multiphysics
  • Modelling fluid structure interaction (FSI) in a thrust bearing


Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
Lectures, Computer based labs, Hand-in assignments.

If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
Hand-in assignments presented in technical reports in English and during oral presentation in English. Individual oral  examination.

Cannot be included in the degree together with M7024T Simulations in tribology.

Andreas Almqvist

Transition terms
The course M7033T is equal to M7024T

Literature. Valid from Autumn 2020 Sp 1 (May change until 10 weeks before course start)
Scientific Computing with applications in Tribology available in DiVA :

Course offered by
Department of Engineering Sciences and Mathematics

CodeDescriptionGrade scaleCrStatusFrom periodTitle
0001AssignmentsU G#5.00MandatoryA20
0003Online examinationG U 3 4 52.50MandatoryA21

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.

Syllabus established
by HUL Niklas Letho 14 Feb 2020

Last revised
by Head Faculty Programme Director Niklas Lehto 17 Feb 2021