Mesh generation algorithm involving irregularly contoured regions for numerical simulations of partial differential equations by finite differences

Resumo

This work proposes a mesh generation algorithm, involving irregular contours. In this algorithm, the
contour of the physical domain is approximated by mesh segments, allowing numerical simulations of partial
differential equations using the finite difference method. Hence, the first code analyzed each node in the mesh,
using two loops. However, this algorithm was impracticable for a mesh with many nodes, as a consequence of
the high number of operations, which let the algorithm slow. As a possibility to reduce the computational cost,
the algorithm was adapted to use only one repetition structure. In order to reduce numerical calculations, the new
algorithm calculates the slope of the line defined by a known point of the irregular contours and the neighboring
vertices. Then the algorithm calculates the line points and the shortest distance from these points to a mesh
node, thus generating a point of the approximate contour. This process is repeated until the approximate contour
is obtained. Algorithm results are presented using four geometries. In these figures, the approximated contour
properly describes the irregular given contour.