Breno Mota Sarmento

Abstract

Accurate estimation of the mean curvature of continuous interfaces is essential in numerical simulations of two-phase flows, in which surface tension forces depend directly on the interface curvature. In this work, the interface is discretized by sur- face meshes, with triangular meshes being considered in the experiments, on which numerical curvature estimation methods are applied. This study presents the im- plementation of an Algebraic Quadratic Fitting Curvature (AQFC) method and its comparative analysis with the Laplace-Beltrami operator discretized via the Fi- nite Element Method (FEM) for computing mean curvature on discretized surfaces. Canonical geometries, discretized with different levels of refinement, were used as test cases, with validation against analytical solutions. The effects of neighbor- hood size in AQFC, mesh regularity, and the sensitivity of the methods to irregular discretizations were investigated. The results indicate that AQFC exhibits greater robustness and stability on irregular meshes, whereas the Laplace-Beltrami opera- tor discretized via FEM maintains high computational efficiency on well-structured meshes.

Advising

FAPERJ · Advisors: Anjos, G. R.; Barbedo, D. V.