GMSH EMBED VOLUME CODE
GMSH EMBED VOLUME FREE

This method gives second order convergence, albeit at a fairly high price in terms of complexity of the implementation. In 2D the method has been extended to unstructured meshes Ito.2014 and in 3D a so-called Embedded Height Function (EHF) approach was invented Ivey.2015, where the VOF field is geometrically mapped onto an overlapping hexahedral mesh on which the height function and its derivatives can then be calculated. Height functions are second order accurate in curvature and interface normal calculation but only work with hexahedral structured meshes in 3D. The derivative is calculated by finite difference operators. Currently, the most accurate approach for the estimation of the normal vector and the curvature is the height function method in which the volume fractions in columns of cells are integrated by direction (x,y,z). However, the method needs a two dimensional minimizer in three dimensions which complicates the implementation and makes the method numerically demanding.

This delivers accurate results on all mesh types in three dimensions. The error of the calculated volume fraction in the neighbouring cells is minimized by changing the orientation of the plane. The plane is used to calculate a volume fraction. In the efficient least squares volume-of-fluid interface reconstruction algorithm (ELVIRA) Pilliod.2004 an interface plane is projected into the neighbouring cells. This method is easy to implement and works in three dimensions and on unstructured meshes but lacks accuracy. In the widely used method by Youngs Youngs.1982, the normal vector is calculated from the gradient of the volume fraction. Several approaches for the computation of the normal vector of the plane can be found in literature. The resulting surface lacks C 0 continuity. 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. Models with an infinitesimal thick interface comprise of two steps: Interface reconstruction and interface advection. in OpenFOAM and Fluent but are often not sufficiently accurate. Models using finite interface thickness are easier to implement and are still used today e.g. The volume of fluid method based on the approach of Hirt Hirt.1981 can be divided into two categories: One with a finite interface thickness and the other with infinitesimal interface thickness. The volume of fluid method is strictly mass conservative but accurate models are harder to implement. However, in practice it allows for good predictions if the discretization is fine enough so that the mass loss can be neglected. A prominent weakness of the level set is its lack of strict mass conservation which is caused by the fundamental problem that the signed distance function is not a passive tracer field. The volume of fluid and level set approaches do not suffer from these problems and are the most commonly used interface methods for practical engineering applications. The first two methods are not optimal for large interface deformation and are difficult to implement.

GMSH EMBED VOLUME FREE

Several different approaches are used to model the free surface Worner.2012 : moving meshes, marker points, level set, phase fields and volume of fluid. The first numerical models were developed in the 1970вЂ™s and the difficulties of this subject are reflected in the continued high level of activity within the research field.

GMSH EMBED VOLUME CODE

Finally, an OpenFOAM based code library with implementations of the proposed schemes is provided with this paper.ДЇree surface simulations can provide highly valuable quantitative and qualitative insights in a large variety of engineering applications. The implementation of the proposed interface reconstruction scheme is straightforward and the computational cost is low. Second order convergence with reduced absolute errors is obtained for simple test cases on all the mentioned mesh types. The new scheme is combined with the interface advection step of the recently developed isoAdvector algorithm. In 3D the second order convergence is verified with reconstruction of a sphere on structured hexahedral meshes and on unstructured tetrahedral and polyhedral meshes. In 2D this is verified with reconstruction of a circle on structured quadrilateral meshes and on unstructured triangular and polygonal prism meshes. 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 в€ћ error norm. In this paper we introduce a novel computational interface reconstruction scheme based on calculation of a reconstructed distance function (RDF). There is, however, still a need for improved simulation methods. Simulations involving free surfaces and fluid interfaces are highly important for many engineering subjects.

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