Numerical Methods for Lubricated Contact Problems

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Lubrication is the process of reducing friction or wear between two moving bodies by applying a lubricant. However, even a lubricant cannot avoid contact between the solid surfaces at all times, and elastic or plastic deformation may take place. The structure of the surfaces changes over time by wear and this affects the properties of the sliding process. Applications are to be found everywhere in our daily life: a piston moving inside a cylinder, a gear-wheel propelled by a wind turbine, a chain moving heavy loads, or a vehicle bearing.


Further information

The lecture will be organized in cooperation with the Chair for Computational Analysis of Technical Systems (CATS). For more information please visit the website of CATS.


Target Audience

Lecture “Numerical Methods for Lubricated Contact Problems” is an elective course suitable for students in the Master programs “Computational Engineering Science”, “Simulation Sciences”, “General Mechanical Engineering”, and others.



The lecture focuses on how one can tackle lubricated contact problems numerically. We will start with the numerical solution of the Reynolds equations and the similarity theory of the lubricated Hertzian contact, and move on to rough surface computations and elasto-plastic contact mechanics, and finally look at today's most advanced methods for lubricated contact based on finite element methods and computational fluid dynamics. In the practical sessions, we will use the commercial solver FIRST to gain some first-hand experience with numerically solving lubricated contact problems and apply the methods discussed during the lecture.


  • Introduction to coupled systems and respective numerical solution procedures, monolithic and partitioned solution strategy, system elimination, co-simulation
  • Fluid system: differential equations and numerical schemes, acceleration and stabilization techniques
  • Structural system: differential equations and numerical schemes, contact models
  • Mesh generation and mesh deformation algorithms, mesh vanishing techniques
  • Coupling conditions and enforcement, spatial and temporal coupling, finite interpolation, dual mortar method, acceleration techniques, stabilization methods, predictor-corrector schemes
  • Solution strategies for thermoelastic deformations, realization of different time scales
  • Multidisciplinary design optimization for lubricated contact problems

For more information please visit the Website of CATS.