Hybrid grid generation for viscous flow analysis

SUMMARY Cartesian grid with cut-cell method has drawn attention of CFD researchers owing to its simplicity. However, it suffers from the accuracy near the boundary of objects especially when applied to viscous flow analysis. Hybrid grid consisting of Cartesian grid in the background, body-fitted layer near the object, and transition layer connecting the two is an interesting alternative. In this paper, we propose a robust method to generate hybrid grid in two-dimensional (2D) and three-dimensional (3D) space for viscous flow analysis. In the first step, body-fitted layer made of quadrangles (in 2D) or prisms (in 3D) is created near the object's boundary by extruding front nodes with a speed function depending on the minimum normal curvature obtained by quadric surface fitting. To solve global interferences effectively, a level set method is used to find candidates of colliding cells. Then, axis-aligned Cartesian grid (quadtree in 2D or octree in 3D) is filled in the rest of the domain. Finally, the gap between body-fitted layer and Cartesian grid is connected by transition layer composed of triangles (in 2D) or tetrahedrons (in 3D). Mesh in transition layer is initially generated by constrained Delaunay triangulation from sampled points based on size function and is further optimized to provide smooth connection. Our approach to automatic hybrid grid generation has been tested with many models including complex geometry and multi-body cases, showing robust results in reasonable time. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  R. Löhner,et al.  Generation of viscous grids at ridges and corners , 2009 .

[2]  Kazuhiro Nakahashi,et al.  Unstructured Mesh Generation For Viscous Flow Computations , 2002, IMR.

[3]  Alper Yilmaz,et al.  Level Set Methods , 2007, Wiley Encyclopedia of Computer Science and Engineering.

[4]  William N. Dawes,et al.  Viscous layer meshes from level sets on cartesian meshes , 2007 .

[5]  Yannis Kallinderis,et al.  Hybrid grid generation for turbomachinery and aerospace applications , 2000 .

[6]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[7]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[8]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[9]  Seyoun Park,et al.  Efficient generation of adaptive Cartesian mesh for computational fluid dynamics using GPU , 2011 .

[10]  William N. Dawes,et al.  Using Level Sets as the Basis for a Scalable, Parallel Geometry Engine and Mesh Generation System (Invited) , 2009 .

[11]  A. Malan,et al.  A cut‐cell non‐conforming Cartesian mesh method for compressible and incompressible flow , 2007 .

[12]  Mohamed S. Ebeida,et al.  A new fast hybrid adaptive grid generation technique for arbitrary two‐dimensional domains , 2010 .

[13]  Zhi J. Wang,et al.  Anisotropic Solution-Adaptive Viscous Cartesian Grid Method for Turbulent Flow Simulation , 2002 .

[14]  D. Thompson,et al.  Quality improvements in extruded meshes using topologically adaptive generalized elements , 2003 .

[15]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[16]  Gerald Farin,et al.  Curves and surfaces for cagd , 1992 .

[17]  H. Xia,et al.  Finite volume distance field and its application to medial axis transforms , 2010 .

[18]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[19]  Bernd Hamann,et al.  Curvature Approximation for Triangulated Surfaces , 1993, Geometric Modelling.

[20]  Timothy J. Baker,et al.  Mesh generation: Art or science? , 2005 .

[21]  Andrew Gary,et al.  GENERALIZED PRISMS FOR IMPROVED GRID QUALITY , 2001 .

[22]  M. Leatham,et al.  Automatic mesh generation for rapid-response Navier-Stokes calculations , 2000 .

[23]  Zhi J. Wang,et al.  A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes , 2003 .

[24]  Kozo Fujii,et al.  Improvements in the Reliability and Efficiency of Body-fitted Cartesian Grid Method , 2009 .

[25]  Kyle Chand,et al.  Component‐based hybrid mesh generation , 2005 .

[26]  Min-Yang Yang,et al.  Offset Triangular Mesh Using the Multiple Normal Vectors of a Vertex , 2004 .

[27]  Yannis Kallinderis,et al.  Hybrid grids for viscous flows around complex 3-D geometries including multiple bodies , 1995 .

[28]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[29]  J. Peiro,et al.  Adaptive remeshing for three-dimensional compressible flow computations , 1992 .

[30]  Ulisses T. Mello,et al.  Three-Dimensional Constrained Delaunay Triangulation: a Minimalist Approach , 1999, IMR.

[31]  Paul G. Tucker,et al.  Level sets for CFD in aerospace engineering , 2010 .

[32]  Solomon Eyal Shimony,et al.  3D scan-conversion algorithms for voxel-based graphics , 1987, I3D '86.

[33]  Oliver Gloth,et al.  Level Sets as Input for Hybrid Mesh Generation , 2000, IMR.