Unstructured triangular surface grid generation and intrinsic grid analysis using rational triangular patches

Abstract

Purpose

To focus on grid generation which is an essential part of any analytical tool for effective discretization.

Design/methodology/approach

This paper explores the application of the possibility of unstructured triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements using piecewise polynomial parametric surfaces which interpolate prescribed R³ scattered data using spaces of parametric splines defined on R² triangulations in the case of surfaces in engineering sciences. The method is based upon minimizing a physics‐based certain natural energy expression over the parametric surface. The geometry is defined as a set of stitched triangles prior to the grid generation. As for derivational continuities between the two triangular patches C⁰ and C¹ continuity or both, as per the requirements, has been imposed. With the addition of a penalty term, C² (approximate) continuity can also be achieved. Since, in this work physics‐based approach has been used, the grid is analyzed using intersection curves with three‐dimensional planes, and intrinsic geometric properties (i.e. directional derivatives), for derivational continuity and smoothness.

Findings

The triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements has been implemented in this paper for surfaces in engineering sciences.

Practical implications

This paper deals with the important problem of grid generation which is an essential part of any analytical tool for effective discretization. And, the examples to demonstrate the theoretical model of this paper have been chosen from different branches of engineering sciences. Hence, the results of this paper are of practical importance for grid generation in engineering sciences.

Originality/value

The paper is theoretical with worked examples chosen from engineering sciences.

Citation

Sharma, R. and Sha, O.P. (2005), "Unstructured triangular surface grid generation and intrinsic grid analysis using rational triangular patches", Engineering Computations, Vol. 22 No. 7, pp. 745-782. https://doi.org/10.1108/02644400510619521