Robust intersection of hexahedral meshes and triangle meshes with applications in finite volume methods

F. Svelander. Licentiate thesis, Chalmers University of Technology and University of Gothenburg, supervisors A. Mark and A. Logg, August 2016.


The topic of this thesis is the intersection of a structured hexahedral grid and one or more triangle meshes. The interest in the problem has arisen in connection with a finite volume method for simulation of conjugated heat transfer. In the particular finite volume method, axis-aligned hexahedra are used for the discretization of the simulation domain, and solids are represented by triangle meshes. The heat equation is discretized over the hexahedral cells. Special treatment is needed in the cells that are intersected by the surface of the solid. In these cells, the solid temperature is found after discretization of the heat equation over the solid part of the cell.

To implement the above, it is of great importance to find the geometry of the cut cells. Of particular interest is the solid volume fraction of a cell, and the solid area fraction of the cell faces. The solid volume fraction is defined as the fraction of the hexahedral cell that is intersected by the solid. Similarly, the solid area fraction is defined for each cell face as the fraction of the face that is intersected by the solid.

Two algorithms for calculation of the solid volume fraction and the solid area fractions are presented. One algorithm is exact, and the other is approximate. The algorithms are extended to handle double surfaces, which is a common mesh degeneracy in engineering applications. A double surface is two layers of coplanar triangles, formed when the triangles are put on top of each other.

The handling of double surfaces is an extension of similar algorithms, which only handle non degenerate triangle meshes. This work is a step towards an algorithm that can be used with such meshes without preprocessing through a repair algorithm. A mesh repair method could be adopted, if available, but that is not always desirable since the existing repair algorithms could fail in removing the degeneracies without introducing unwanted side effects. This motivates the need for an algorithm that handles degenerate triangle meshes.

The algorithms are validated against a geometry from an industrial application, which includes a double surface. It is concluded that the exact algorithm is independent of cell size, while the approximate algorithm is second order accurate for the test case that has been studied. It is further concluded that the methods handle the major problems with double surfaces.

Finally, it is described how the algorithms are used in a finite volume framework for simulation of conjugated heat transfer.

Photo credits: Nic McPhee