Streamline integration as a method for two-dimensional elliptic grid generation

TL;DR

This paper introduces a new parallelizable numerical algorithm for generating structured elliptic grids in doubly connected domains, ensuring orthogonality to boundaries and allowing control over cell distribution, with high precision and efficiency.

Contribution

The paper presents a novel, efficient, and parallelizable method for constructing structured elliptic grids with boundary orthogonality and adjustable cell distribution in doubly connected domains.

Findings

Grids constructed with monitor metrics show superior quality.

The algorithm achieves high accuracy up to machine precision.

The method is easy to implement with elementary numerical techniques.

Abstract

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The resulting grids are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach.