Numerical Simulation of Contact Problems with Fluid-Structure Interaction

• Applicant: Privatdozent Dr. Stefan Frei
• Subject Area: Mathematics
• Term: from 2017 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 367992309

Contact problems between different solid structures arise in many physical processes in nature, engineering or medicine. In most situations, a liquid or gas lies between the structures before and after or even in form of a very thin fluid layer during the contact. This fluid might have a significant effect on the contact dynamics. Therefore, in many cases a full fluid-structure interaction (FSI) problem has to be considered.In this project, we develop an accurate and robust numerical framework for the simulation of FSI with contact. While a vast amount of literature exists for both FSI and contact mechanics alone, many open questions persist for their combination. Many of the standard numerical methods commonly used for FSI are not able to deal with the topology changes of the fluid domain at the time of contact. Promising approaches that are able to deal with contact are a Fully Eulerian approach and Lagrangian-Eulerian techniques based on a coupling by means of Nitsche's method or using Lagrange multipliers. However, very few studies exist for all these approaches considering the case of contact. In this project, we will compare the available numerical methods for both the case of thin-walled structures of co-dimension one and thick structures of equal dimension. For discretisation, we plan to use a geometrically unfitted finite element approach that is able to deal with the moving interfaces accurately without re-meshing.To model contact, new approaches based on an augmented Lagrangian formulation will be investigated and compared against standard methods using Lagrange multipliers or a penalty force. The application of this method in the context of FSI is novel.The final objective of the project is to derive and analyse numerical methodologies for fluid-structure interactions with contact both in the case of thick and thin structures and to apply it to applications of practical interest, such as the closure of the mitral valves in the coronary artery.

• DFG Programme: Research Fellowships
• International Connection: United Kingdom
• Host: Professor Erik Burman