A structured tri‐tree search method for generation of optimal unstructured finite element grids in two and three dimensions

Abstract

SUMMARYA new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea-Skagerrak area.

Adaptive Linearization and Grid Iterations With the Tri-Tree Multigrid Refinement-Recoarsement Algorithm for the Navier-Stokes Equations

“…6 The purpose of the present work is eventually to develop algorithms suited for multiprocessing. In previous papers a new tri-tree grid generator algorithm 6 and a new incomplete preconditioning algorithm 7 have been described. The tri-tree grid generation algorithm was well suited to organizing and structuring grids at different levels of refinement.…”

Parallel ILU preconditioning, a priori pivoting and segregation of variables for iterative solution of the mixed finite element formulation of the Navier–Stokes equations

“…The equations corresponding to the velocity degrees of freedom are assembled ÿrst in the global matrix, and at last the equations corresponding to the pressure degrees of freedom which are the cause of the indeÿniteness [1,2]. During the parallel computation, adaptive meshing [3,4] is applied to improve the ÿnite element approximation and to improve the convergence performance of the iterative solver [5].…”

Numerical simulation of fluid flows using an unstructured finite volume method with adaptive tri‐tree grids

“…For viscous and unsteady ow problems involving complex boundaries, it is desirable to use a grid generation algorithm that can automatically divide the uid domain into elements. Wille [1] described two-dimensional triangular and three-dimensional tetrahedral grid generation using the tri-tree and the tetra-tree methods respectively. The hierarchical data structure of tri-tree and tetra-tree reference numbers allows the algorithm to perform both up-and downsearches in grid adaptation as required.…”