Hybrid grid generation for viscous flow analysis

Abstract

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.

Hybrid volume completion with higher-order Bézier elements

“…This idea is applied to complex turbomachinery and aerospace geometries in Khawaja and Kallinderis (2000). Similar idea is applied to viscous flow analysis in Park et al (2013) where a transition layer composed of tetrahedra is used to connect the gap between prisms near the object's boundary and an axis-aligned Cartesian grid in the rest of the domain. Hmorph (Owen and Saigal, 2000) created a hexahedral-dominant mesh by iteratively converting the input tetrahedral mesh into a hexahedral mesh using an advancing front technique.…”

On the ‘most normal’ normal—Part 2

“…Note the similarity between the original sweeping of Fortune [35], Yao et al [30] outside in sweeping, a boundary layer mesh extrusion [10][11][12][13] and a fast marching method [22]. They all rely on the hyperbolic character of the Eikonal equation.…”

“…A different viewpoint is to consider the triangulation as a discrete object without specific connections to a smooth surface. In the context of a boundary layer mesh generator, prisms are extruded from the surface triangulation along the point normals [10][11][12][13]. An accurate computation of the normal is required, particularly along corners and ridges, since a bad normal may lead to a premature interruption of the boundary layer extrusion, a loss of orthogonality, or the creation of low quality elements.…”

Hybrid grid generation for viscous flow simulations in complex geometries

“…With respect to the generation of unstructured meshes, either the advancing front technique (AFT) based approach [8] or the Delaunay triangulation (DT) based approach [9][10][11] could be adopted. In some studies, it has been suggested to first fill an axis-aligned Cartesian mesh in the far field of viscous walls and then connect the boundary layer mesh and the Cartesian mesh with a few transition layers of unstructured elements [12][13][14][15].…”