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 of 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 two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source.
Highlights
In this paper, we address the numerical challenge of advancing a surface moving in a prescribed velocity field
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
We present the results of simple test cases with isoAdvector
Summary
We address the numerical challenge of advancing a surface moving in a prescribed velocity field. We will refer to this as the interface advection problem, because the surface often constitutes an interface e.g. between two fluids. Simple as the problem may appear, there is a large variety of problems in science, engineering and industry where its solutions are far from trivial. Our motivation for addressing this problem is rooted in our usage of computational fluid dynamics (CFD) as a practical engineering tool for calculating wave loads on coastal and marine.
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