Geometrically exact methods for fluid-structure interaction

• Applicant: Professor Marek Behr, Ph.D.
• Subject Area: Mechanics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 249132206

The methods developed in the proposed project will allow the solution of a class of fluid-structure-interaction problems via practical partitioned methods, which could up to now be solved only with monolithic methods. This can be achieved by guaranteeing that both the fluid and structure sides use an identical boundary description. For this purpose, methods based on Non-Uniform Rational B-Splines (NURBS) are used on both fluid and structural sides and coupled at the interface. Beyond that aspect, the separation of solvers for the fluid and the structure remains possible. Using partitioned approaches allows the integration of existing and specialized single-field solvers into an overall solution system. Unfortunately, different surface discretization in presents a challenge in such solvers. The necessary methods to project physical variables from one side to the other reduce the stability of partitioned approaches compared to more elaborate monolithic approaches. So far this problem has not been addressed satisfactorily. By applying approaches based on NURBS, an exact geometry of the wetted surface on both sides can be guaranteed and the transfer errors can be reduced or eliminated. The proposed concept is inspired by the isogeometric analysis (IGA), which has been gaining popularity in the structural analysis in recent years. Performing the numerical load analysis directly on the geometric formulation used during the design process is the main advantage of this method, and it is used in the suggested project on the structural side. Because the generation of suitable volume discretizations has been achieved in IGA only for relatively simple geometries, its application in fluid mechanics is limited. However, extending conventional methods with a NURBS-based boundary formulation can preserve many advantages of the method. This concept is followed in the NURBS-enhanced Finite-Element Method (NEFEM), which will be used in the proposed project on the fluid side. The project involves the development of the essential transfer methods. One intermediate step is the extension of existing methods while using a conventional method on the other, fluid or structural, side. The advantages of the developed methodology will be demonstrated on academic problems and on real-world applications. Advances in robustness and accuracy are expected by the incorporation of the innovative single-field solvers and by the reduction of errors in the transfer methods at the interface. In addition to the method development, a workshop is planned to support the scientific communication about current state of the art in the field of fluid-structure interaction. During this workshop, groundbreaking methods will be presented and discussed by international experts; the workshop will also provide a platform for young academics.

• DFG Programme: Research Grants