CHANNELS FLOW MODELING BY USING ISOGEOMETRIC ANALYSIS

In this work, two types of flow are modeled by the isogeometric analysis (IA) method. The first problem involved is to find the velocity distribution of the uniform flow in a sloped channel, and the second one is the irrotational flow around the circular and rectangular obstacles. The formulation is derived, and its differences with the finite element (FE) method are explained. In the IA method, the unknown function of the governing differential equation and the domain boundaries are approximated by NURBS (non-uniform rational Bsplines). Due to the ability of NURBS in constructing curves and surfaces with high precision, channels with complicated boundaries can easily be considered. The IA results are compared with the standard finite element, and their accuracy is demonstrated by means of several examples. Furthermore, the effects of some of the IA parameters such as the irregularity of the control point grid, different knot vectors, and number of control points are also discussed.

[1]  W. Wall,et al.  Isogeometric structural shape optimization , 2008 .

[2]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[3]  David Salomon,et al.  Curves and surfaces for computer graphics , 2005 .

[4]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[5]  Behrooz Hassani,et al.  ISOGEOMETRICAL SOLUTION OF LAPLACE EQUATION , 2009 .

[6]  Thomas J. R. Hughes,et al.  Isogeometric shell analysis: The Reissner-Mindlin shell , 2010 .

[7]  Thomas J. R. Hughes,et al.  NURBS-based isogeometric analysis for the computation of flows about rotating components , 2008 .

[8]  Mostafa Khanzadi,et al.  Isogeometric shape optimization of three dimensional problems , 2009 .

[9]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[10]  T. Hughes,et al.  B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements , 2008 .

[11]  John A. Evans,et al.  Robustness of isogeometric structural discretizations under severe mesh distortion , 2010 .

[12]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[13]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[14]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[15]  Nathan Ida,et al.  Introduction to the Finite Element Method , 1997 .

[16]  D. F. Rogers,et al.  An Introduction to NURBS: With Historical Perspective , 2011 .

[17]  Les A. Piegl,et al.  The NURBS book (2nd ed.) , 1997 .

[18]  Josef Hoschek,et al.  Handbook of Computer Aided Geometric Design , 2002 .