This paper presents a novel variational formulation to simulate linear free-surface flow. The variational formulation is suitable for higher-order finite elements and higher-order and higher-continuity shape functions as employed in Isogeometric Analysis (IGA). The novel formulation combines the interior and free-surface problems in one monolithic formulation. This leads to exact energy conservation and superior performance in terms of accuracy when compared to a traditional segregated formulation. This is confirmed by the numerical computation of traveling waves in a periodic domain and a three-dimensional sloshing problem. The isogeometric approach shows significant improved performance compared to traditional finite elements. Even on very coarse quadratic NURBS meshes the dispersion error is virtually absent.
@article{arxiv.1902.07113,
title = {Isogeometric analysis of linear free-surface potential flow},
author = {I. Akkerman and J. H. A. Meijer and M. ten Eikelder},
journal= {arXiv preprint arXiv:1902.07113},
year = {2020}
}