Isogeometric analysis of free-surface flow

Abstract

This paper presents the first application of isogeometric analysis, a new computational technology built on higher-order and higher-continuity basis functions employed in Computer-Aided Design and computer graphics, to the computation of free-surface phenomena described using the level set approach. The method is based on the variational framework that is suitable for discretization by standard finite elements as well as the basis functions employed in isogeometric analysis. The underlying numerical formulation globally conserves mass and preserves a sharp air–water interface for the entire length of the simulation. The numerical tests indicate that the proposed methodology gives an accurate description of the free-surface behavior in both quasi-steady and dynamic regimes. Furthermore, very good per-degree-of-freedom accuracy is obtained when higher-order and higher-continuity isogeometric discretizations are employed in free-surface computations.