A numerical investigation is performed here using a NURBS-based finite element formulation applied to classical Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems. Model capabilities related to refinement techniques are analyzed using a finite element formulation with NURBS (non uniform rational B-splines) basis functions, where B-splines and low-order Lagrangian elements can be considered as particular cases. An explicit two-step Taylor-Galerkin model is utilized for discretization of the fundamental flow equations and turbulence is considered using Large Eddy Simulation (LES) and the Smagorinsky's sub-grid scale model. FSI is considered using an ALE kinematic formulation and a conservative partitioned coupling scheme with rigid body approach for large rotations is adopted. CFD and FSI applications are analyzed to evaluate the accuracy associated with the different refinement procedures utilized. Results show that high order basis functions with appropriate refinement and non-uniform parameterization lead to better predictions, compared with low-order Lagrangian models.
The present work proposes the development of numerical tools for solving fluid-structure interaction (FSI) problems where the structure is coupled with cables. For the numerical treatment of fluids in incompressible flow, the Navier-Stokes and continuity equations are discretized using a semi-implicit version of the characteristic-based split (CBS) method in the context of the finite element method (FEM), where linear tetrahedral elements are used. In the presence of moving structures, the flow equations are described through an arbitrary Lagrangian-Eulerian (ALE) formulation and a numerical scheme of mesh movement is adopted. The structure is treated through a three-dimensional rigid body approach and the cable through an elastic model with geometric nonlinearity and spatial discretization by the nodal position finite element method (NPFEM). The system of equations of motion can be temporally discretized using the implicit Newmark and generalized-α methods and a partitioned coupling scheme is used taking into account fluid-structure and cable-structure couplings. The algorithms proposed here are verified using numerical applications.
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