Fluid-Structure Interaction

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Spectral elements are p-type element which can provide better accuracy and faster convergence. However, applications of these elements make conformation to discontinuities in the function or its derivative difficult. The eXtended Finite Element Method (XFEM) recently developed at Northwestern University can easily treat the arbitrarily aligned discontinuities, i.e. independent of the mesh, for both the function and its derivative. A spectral finite element with arbitrary discontinuities is developed. We show an optimal convergence rate of the spectral element for straight discontinuities and slightly suboptimal convergence rate for curved discontinuity in the energy norm error. A variational principle is developed for fluid-structure interaction of bodies. The variational principle is applicable to models where the fluid is described by Eulerian coordinates while the solid is described by Lagrangian coordinates, which suits their intrinsic characteristics. The momentum equation and the coupling are unified in one weak form. This weak form is in accord with the standard Finite Element Method (FEM) and is easy to implement. The method enables the fluid and solid meshes to be arbitrary and there is no limit on the extent of the deformation of the solid. Although a compressible viscous fluid formulation is implemented here, the method can be extended to incompressible fluids. Both explicit and implicit time integration can be used with this method. The constraint method for fluid-structure interaction is further developed. As for the variationally consistent method for the fluid-structure interaction problem, the meshes for the fluid and solid are independent. Eulerian coordinates are used for the fluid and Lagrangian coordinates for the solid. The coupling is furnished through the enforcement of the continuity equation on the interface by a constraint method. The momentum balance on the interface is supplied by the weak form. The interface integration required by the coupling is regularized by a window function. This avoids the awkward line integration in 2D and surface integration in 3D.

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  • 05/21/2018
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