An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation

We propose an Eulerian framework for modelling fluid-structure interaction (FSI) of incompressible fluids and elastic structures. The model is based on an Eulerian approach for describing structural dynamics. This is achieved by tracking the movement of the initial positions of all 'material' points. In this approach the displacement appears as a primary variable in an Eulerian framework. Our approach uses a technique which is similar to the level set method in so far that it also tracks initial data, in our case the set of initial positions (IP), and from this determines to which 'phase' a point belongs. To avoid the occasional reinitialization of the initial position set we employ the harmonic continuation of the structure velocity field into the fluid domain. By using the IP set for tracking the structure displacement, we can ensure that corners and edges of the fluid-structure interface are preserved well. Based on this monolythic model of the FSI we apply the Dual Weighted Residual (DWR) method for goal-oriented a posteriori error estimation to stationary FSI problems. Examples are presented based on the model and for the goal-oriented local mesh adaptation.

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