Design of adaptive unstructured grids using differential methods

Abstract

Adaptive generation of computational grids can improve the efficiency of mathematical modeling by increasing the accuracy of numerical approximations. The paper describes a method for constructing unstructured grids with adaptation based on differential methods. The application of these methods ensures a smooth distribution of the geometric characteristics of the grid, i.e. the appearance of adjacent cells that differ greatly in size and shape becomes unlikely. To achieve proper adaptation in unstructured grids we use the novel approach based on methodology of adaptive structured grid construction. This approach uses the method of grid construction based on solving inverted Beltrami equation to create mapping of some sample grid domain to the physical area. This mapping is used to construct point set on which the unstructured grid is constructed using Delaunay triangulation method. Thus, the result is unstructured grid with proper adaptation. Adding fault and fractures or other structure elements may be supported by implementing constrained Delaunay triangulation.