关键词: 任意形状网格, 精确几何, 本质边界条件, 数值流形方法, 独立覆盖

Abstract: Finite element meshes should keep regular shape as much as possible, and ensure correct connections through nodes. These requirements pose a great burden to the pre-processing procedure of numerical computations for solving domains with complex shapes. On the other hand, curve boundaries in practical situations are usually discretized into shapes which finite element meshes can describe, resulting in an imprecise simulation of exact geometry defined in CAD. In view of this, cover meshes with arbitrary shapes and arbitrary connections are implemented using Manifold Method based on independent covers. Exact geometric boundaries of CAD models and boundary conditions are simulated in CAE analyses. The solving domain is divided into block meshes with arbitrary shapes which can contain curve boundaries. And two approaches, including analytical integration method with simplexes and numerical integration method, can be used for the block integration. The thin strips for cover overlapping are considered only in the integration process, but are not necessarily involved in the generation of computation models. Essential boundary conditions are strictly applied through boundary strips, including the boundary conditions on curves. Moreover, two numerical examples are given to illustrate the validity of the method. Cover meshes with arbitrary shapes bring about a new path for numerical computations based on exact geometric models and automatic pre-processing procedures.

Key words: meshes with arbitrary shapes, exact geometry, essential boundary conditions, Numerical Manifold Method (NMM), independent covers