Abstract
Abstract 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.
Highlights
The use of finite volume models is still a common practice in the field of Computational Fluid Dynamics (CFD), the Finite Element Method (FEM) has gained some popularity in the last decades with significant advances observed in computers technology
In order to overcome these drawbacks some improvements have been proposed to the finite element formulation, such as the use of NURBS basis functions, which are extensively utilized in Computational Aided Design (CAD)
The present results demonstrate that the control mesh configuration with mesh parameter h = 0.001L is clearly insufficient to reproduce the reference results, independent of the basis function degree utilized
Summary
The use of finite volume models is still a common practice in the field of Computational Fluid Dynamics (CFD), the Finite Element Method (FEM) has gained some popularity in the last decades with significant advances observed in computers technology (see, for instance, Zienkiewicz et al, 2013; Reddy and Gartling, 2010). In order to overcome these drawbacks some improvements have been proposed to the finite element formulation, such as the use of NURBS (non uniform rational B-splines) basis functions, which are extensively utilized in Computational Aided Design (CAD) (see Piegl and Tiller, 1997) With this improvement, many possibilities with respect to refinement procedures may be conceived, in spite of some shortcomings that are observed. A NURBS finite element formulation for CFD applications presents significant improvements over the classical Lagrangian finite element formulation Complex flow phenomena, such as boundary layer and turbulent flows, separation, and reattachment are better reproduced considering that different flow regions can be discretized using distinct combinations of degree and continuity order associated with the interpolation functions. Notice that the classical p-refinement utilized in finite element modeling must be initially applied over basis functions with C0-continuity, while p-refinement for B-spline discretizations can be adopted using any continuity order This aspect cannot be replicated with a standard finite element formulation. Classical CFD and FSI applications are analyzed in order to validate the present methodology, where different refinement procedures are adopted and investigated
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