Rectangular mesh contour generation algorithm for finite differences calculus

TL;DR

This paper introduces a 2D contour generation algorithm for irregular regions that approximates physical domain contours using mesh segments, enhancing finite difference calculations in numerical simulations.

Contribution

The proposed algorithm efficiently generates approximate contours for irregular geometries using known contour points and mesh nodes, suitable for finite difference methods.

Findings

Achieves area difference below 2% with refined meshes.

Requires more nodes for complex geometries.

Effective for irregular boundary approximation.

Abstract

In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a repeating structure that analyzes the known irregular contour coordinates to approximate the physical domain contour by mesh segments. To this end, the algorithm calculates the slope of the line defined by the known point of the irregular contours and the neighboring vertices. In this way, the algorithm calculates the points of the line and its distance to the closest known nodes of the mesh, allowing to obtain the points of the approximate contour. This process is repeated until the approximate contour is obtained. Therefore, this approximate contour generation algorithm, from known nodes of a mesh, is suitable for describing meshes involving geometries with irregular contours and for calculating finite differences in numerical simulations. The contour is evaluated through three geometries, the difference between the areas delimited by the given contour and the approximate contour, the number of nodes and the number of internal points. It can be seen that the increase in geometry complexity implies the need for a greater number of nodes in the contour, generating more refined meshes that allow reaching differences in areas below 2%.