An Immerse Domain Method for Fluid-Structure Interaction with Contact
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We present an embedded approach for the numerical solution of contact problems between multiple elastic structures immersed in a fluid flow. We designed this approach to simulate the full dynamics of a bio-prosthetic heart valve. We model the blood-valve interaction, the blood-aortic wall interaction, and the contact among leaflets during the valve closure. The solid bodies are modeled as hyperelastic anisotropic materials, whereas the fluid is regarded as a Newtonian flow. The mathematical modeling of such material properties and the contact mechanics give rise to a large-scale nonlinear problem that is both challenging and computationally expensive to solve. Furthermore, the assembly of such a system is also challenging due to the requirement of handling coupling conditions between solid and fluid and the contact conditions between solid surfaces which are in contact, in particular in a parallel-computing environment where the geometric data is arbitrarily distributed and unrelated. Our approach employs a parallel-tree search algorithm for assembling the coupling and contact conditions in combination with an immersed domain approach. In particular, we use a localized version of the L2-projection for handling the fluid-structure volumetric coupling and a variant of the mortar method for coupling the surfaces of the structures in contact. Our strategy is verified through numerical benchmarks and finally employed to model the dynamics of a bio-prosthetic heart valve placed in the aortic root.
