Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements

TL;DR

This paper explores interface-tracking methods for free-surface flow simulations using isogeometric analysis, comparing weak and strong boundary condition impositions and various coupling strategies to improve mesh conformity and accuracy.

Contribution

It introduces an isogeometric approach for free-surface flow with boundary condition imposition options and coupling strategies, enhancing interface tracking accuracy.

Findings

Continuous normal vector and velocity are available with NURBS basis functions.

Weak imposition of boundary conditions is feasible with isogeometric analysis.

Different coupling methods impact mesh stability and boundary accuracy.

Abstract

The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options, be dealt with using an interface-tracking approach with the Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A difficult issue that is connected with this type of approach is the determination of a suitable coupling mechanism between the fluid velocity at the boundary and the displacement of the boundary mesh nodes. In order to avoid large mesh distortions, one goal is to keep the nodal movements as small as possible; but of course still compliant with the no-penetration boundary condition. Standard displacement techniques are full velocity, velocity in a specific coordinate direction, and velocity in normal direction. In this work, we investigate how the interface-tracking approach can be combined with isogeometric analysis for the spatial discretization. If NURBS basis functions of sufficient order are used for both the geometry and the solution, both a continuous normal vector as well as the velocity are available on the entire boundary. This circumstance allows the weak imposition of the no-penetration boundary condition. We compare this option with an alternative that relies on strong imposition at discrete points. Furthermore, we examine several coupling methods between the fluid equations, boundary conditions, and equations for the adjustment of interior control point positions.