Streamline integration as a method for two-dimensional elliptic grid generation
For researchers in computational geometry and numerical simulation, this provides an efficient and accurate grid generation method for specific domain types, though it is incremental over existing elliptic grid techniques.
The paper introduces a new numerical algorithm for generating structured elliptic grids in doubly connected domains, achieving boundary orthogonality and machine-precision computation of grid points and Jacobian elements. The monitor metric approach yields the best grid quality in terms of cell size distribution and solution accuracy for elliptic problems.
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.