# Isogeometric analysis of linear free-surface potential flow

## TL;DR

This paper introduces a new isogeometric analysis formulation for linear free-surface potential flow, achieving higher accuracy and energy conservation compared to traditional methods, demonstrated through numerical simulations.

## Contribution

It develops a monolithic variational formulation compatible with IGA, integrating interior and free-surface problems for improved simulation accuracy.

## Key findings

- Exact energy conservation achieved.
- Superior accuracy over traditional finite elements.
- Virtually no dispersion error on coarse meshes.

## Abstract

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.