A NURBS-based immersed methodology for fluid–structure interaction

Abstract

We introduce an isogeometric, immersed, and fully-implicit formulation for fluid–structure interaction (FSI). The method focuses on viscous incompressible flows and nonlinear hyperelastic incompressible solids, which are a common case in various fields, such as, for example, biomechanics. In our FSI method, we utilize an Eulerian mesh on the whole domain and a Lagrangian mesh on the solid domain. The Lagrangian mesh is arbitrarily located on top of the Eulerian mesh in a non-conforming fashion. Due to the formulation of our problem, based on the Immersed Finite Element Method (IFEM), we do not need mesh update or remeshing algorithms. The fluid–structure interface is the boundary of the Lagrangian mesh, but cuts arbitrarily the Eulerian mesh. The generalized- α method is used for time discretization and NURBS-based isogeometric analysis is employed for the spatial discretization on both fluid and solid domains. The information transfer between the two meshes is carried out using the NURBS functions, which avoids the use of the so-called discretized delta functions. The higher order and especially the higher continuity of NURBS functions allow us to deal with severe mesh distortion in the Lagrangian mesh in comparison with classical C0 linear piecewise functions as we prove numerically. Our numerical solutions attain good agreement with theoretical data for free-falling objects in two and three dimensions, which confirms the feasibility of our methodology.