A Computational Method for Sharp Interface Advection

TL;DR

The paper introduces isoAdvector, a novel geometric numerical method for accurately simulating the passive advection of fluid interfaces on arbitrary meshes, improving volume conservation and surface sharpness.

Contribution

It presents the isoAdvector method, combining isosurface modeling and face-interface intersection tracking for precise interface advection on complex meshes.

Findings

High accuracy in volume conservation and surface sharpness

Effective on both structured and unstructured meshes

Open source implementation as an OpenFOAM extension

Abstract

We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists in two parts: First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face-interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple 2D and 3D interface advection problems both on structured and unstructured meshes. The results are very satisfactory both in terms of volume conservation, boundedness, surface sharpness, and efficiency. The isoAdvector method was implemented as an OpenFOAM(R) extension and is published as open source.