Огляд методів генерації дискретних моделей геометричних об’єктів

Abstract

UK: У статті проведено огляд актуальних методів побудови структурованих і блочно-структурованих дискретних моделей геометричних об'єктів. Наведено визначення дискретної моделі (сітки) геометричного об'єкта, її типів та різновидів. Описано загальну послідовність кроків, необхідних для генерації структурованих дискретних моделей геометричних об'єктів, рівння і теорії, на основі яких будуються сітки, спеціальні програмні засоби для генерації сіток, EN: Computer simulations have been widely employed in modem engineering. Such simulations allow to emulate a physical system using numerical analysis. Typical engineering problems employ structural analysis, heat transfer, fluid flow, etc. These problems generally require the solution to boundary value problem for partial differential equations. The numerical solution of a boundary value problem involves dividing the domain of the problem into a collection of subdomains (a discrete model). Generally, a discrete model of a geometric object (aka mesh or grid) is a tessellation of a part of the Euclidean space by simple shapes such as, triangles, quadrilaterals, tetrahedra, hexahedra, etc. There are exists two classes of meshes: structured and unstructured. Structured grids (opposite to unstructured) are identified by regular connectivity. Each element in the structured grid can be addressed by an index. Structured grids typically have the higher degree of quality, better convergence, and require less computational memory. Structured data also allows the use of solution algorithms which are not possible to implement on unstructured data. The objective of this article is to study methods and approaches for an automatic generation of structured discrete models of geometric objects. The article is a review of the most useful methods for the automatic generation of structured and block- structured discrete models of geometric objects. Initially, possible applications of structured grids have been described. In the next section, applications of elliptic, hyperbolic, and parabolic equations for structured grid generation have been studied. The most efficient numerical methods for mesh generation have been also reviewed. In the final section, some engineering applications of structured grids have been discussed.