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.

The performance of interFoam (a widely-used solver within the popular open source CFD package OpenFOAM) in simulating the propagation of a nonlinear (stream function solution) regular wave is investigated in this work, with the aim of systematically documenting its accuracy. It is demonstrated that over time there is a tendency for surface elevations to increase, wiggles to appear in the free surface, and crest velocities to become (severely) over estimated. It is shown that increasing the temporal and spatial resolution can mitigate these undesirable effects, but that a relatively small Courant number is required. It is further demonstrated that the choice of discretization schemes and solver settings (often treated as a "black box" by users) can have a major impact on the results. This impact is documented, and it is shown that obtaining a "diffusive balance" is crucial to accurately propagate a surface wave over long distances without requiring exceedingly high temporal and spatial resolutions. Finally, the new code isoAdvector is compared to interFoam, which is demonstrated to produce comparably accurate results, while maintaining a sharper surface. It is hoped that the systematic documentation of the performance of the interFoam solver will enable its more accurate and optimal use, as well as increase awareness of potential shortcomings, by CFD researchers interested in the general CFD simulation of free surface waves.

Simulations involving free surfaces and fluid interfaces are important in many areas of engineering. There is, however, still a need for improved simulation methods. Recently, a new efficient geometric VOF method called isoAdvector for general polyhedral meshes was published. We investigate the interface reconstruction step of isoAdvector, and demonstrate that especially for unstructured meshes the applied isosurface based approach can lead to noisy interface orientations. We then introduce a novel computational interface reconstruction scheme based on calculation of a reconstructed distance function (RDF). By iterating over the RDF calculation and interface reconstruction, we obtain second order convergence of both the interface normal and position within cells even with a strict L ∞ error norm. In 2D this is verified with reconstruction of a circle on Cartesian meshes and on unstructured triangular and polygonal prism meshes. In 3D the second order convergence is verified with reconstruction of a sphere on Cartesian meshes and on unstructured tetrahedral and polyhedral meshes. The new scheme is combined with the interface advection step of the isoAdvector algorithm. Significantly reduced absolute advection errors are obtained, and for CFL number 0.2 and below we demonstrate second order convergence on all the mentioned mesh types in 2D and 3D. The implementation of the proposed interface reconstruction schemes is straightforward and the computational cost is significantly reduced compared to contemporary methods. The schemes are implemented as an extension to the Computational Fluid Dynamics (CFD) Open Source software package, OpenFOAM R . The extension module and all test cases presented in this paper are released as open source. and are still used today e.g. in OpenFOAM and Fluent R , but are often not sufficiently accurate. Models assuming an infinitesimal interface thickness comprise of two steps: Interface reconstruction and interface advection. The most common reconstruction method is the piecewise linear interface reconstruction method (PLIC), where the interface within a cell is represented by a plane cutting the cell into two subcells. The resulting surface lacks C 0 continuity. Several approaches for the computation of the normal vector of the plane can be found in literature. In the widely used method by Youngs [3], the normal vector is calculated from the gradient of the volume fraction field. This method is easy to implement, also on three dimensional unstructured meshes, but lacks accuracy. In the least squares volume-of-fluid interface reconstruction algorithm (LVIRA) [4] an interface plane is projected into the neighbouring cells. The plane is used to calculate a volume fraction. The error of the calculated volume fraction in the neighbouring cells is minimized by changing the orientation of the plane. This delivers accurate results on all mesh types in three dimensions. However, the method needs a two dimensional minimizer in three dimensions which complicates the implementation and makes the m...

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