Implementation of volume correction and mesh relaxation algorithms in isogeometric boundary element formulation for modeling droplet motion

Abstract

Numerical techniques are required to understand the details of the flow that are infeasible or difficult for experimental techniques. The boundary element method is an advantageous technique to model interfacial dynamics problems due to its boundary-only discretization feature. In this study, isogeometric boundary element formulation is proposed to model the evolution of the interface of a droplet in 2D confined flows with a variable viscosity ratio. To reduce the computational cost while maintaining high accuracy, low spatial resolutions are used. However, simply reducing the resolution leads to non-physical results such as violating the incompressibility condition which becomes a severe problem for specific viscosity ratios. In this work, stabilization algorithms are developed to address the numerical artifacts at low resolutions. The volume correction algorithm is employed to avoid the drift in the volume of fluid enclosed in the droplet. Mesh relaxation technique is utilized to preserve the mesh quality for a range of Capillary numbers. The proposed method that is systematically integrating these algorithms offers a unified way to model the dynamics of droplets with accurate geometry representation with a compressed meshing procedure at low spatial resolutions.