A new fast hybrid adaptive grid generation technique for arbitrary two‐dimensional domains

Abstract

SUMMARYThis paper describes a new fast hybrid adaptive grid generation technique for arbitrary twodimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution-based adaptive grid is desired. The resulting grid is quad-dominant and ready for the application of finite-element, multigrid, or line-relaxation methods. All of the internal angles in the final grid have a lower bound of 45• and an upper bound of 135• . Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach.

Hybrid grid generation for viscous flow analysis

“…Zhang et al [5] Quad/Tri/Cartesian Advancing front method 2D Wang et al [6] Hexa/Tetra Advancing front method 3D Khawaja et al [10,11] Prism/Tetra Automatic receding 3D C advancing front method Dawes et al [8,9] Hexa/Cartesian Level set method 3D Gloth et al [12] Quad/Tri/Cartesian Level set method 2D Pattinson et al [13] Cartesian Cut-cell, dual-mesh 2D Ebeida et al [3] Quad/Tri Spatial decomposition We assume that the input object is given as a piecewise linear representation, such as the point sequence curves in 2D and triangular meshes in 3D. Let B = { 1 .…”

“…The level set [14,15] is the mathematical model, which describes the behavior of fronting boundaries varied by time. Given an interface .t/ in R n (n=2, 3) bounding an open region .t / and moving along time t , let an implicit functionˆ.p, t/ have the signed distance from p to .t/, and 895 the plus sign is chosen if p is outside .t /. Given an interface .t/ in R n (n=2, 3) bounding an open region .t / and moving along time t , let an implicit functionˆ.p, t/ have the signed distance from p to .t/, and 895 the plus sign is chosen if p is outside .t /.…”

“…The pros and cons of each type are well discussed in the literatures such as Baker [2]. For this reason, a hybrid mesh consisting of a body-fitted structured mesh layer and an unstructured background mesh has gained the attention of CFD researchers for viscous flow analysis in recent years [3][4][5][6][7][8][9][10][11][12][13] including its use in several commercially available software programs such as VisCART, Harpoon, and GDT. However, a structured grid makes unnecessarily dense elements in areas far from focal objects to achieve the resolution required in the critical part of the domain.…”

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

“…Three typical approaches are briefly discussed here. The first approach is to subdivide the higher level quadtree cells next to a hanging node into smaller triangular and quadrilateral elements to enforce compatibility . Additional nodes may be added to improve the mesh quality and/or reduce the number of element types.…”

“…The first approach is to subdivide the higher level quadtree cells next to a hanging node into smaller triangular and quadrilateral elements to enforce compatibility. [16][17][18] Additional nodes may be added to improve the mesh quality and/or reduce the number of element types. The second approach is to create special conforming shape functions for cells with hanging nodes to ensure the displacement compatibility.…”