Isosurface extraction for piecewise-linear reconstruction of complex interfaces on arbitrary grids

Abstract

In the field of volume of fluid type schemes, there is still great room for improvement in the accuracy of the methods used to reconstruct interfaces, especially when highly complex interfaces are involved. Isosurface extraction is exploited in a series of piecewise-linear interface reconstruction methods to simulate complex interface dynamic problems on arbitrary grids, and high-order surface patches are applied to achieve significantly improved accuracy. Isosurface extraction is also used to choose a convenient set of neighboring cells, hereafter called reconstruction stencil, for the reconstruction of highly curved interfaces when using well-known linearity-preserving methods. The relevance of the proper selection of the reconstruction stencil is highlighted, showing that the convergence of formal second-order methods can deteriorate when inappropriate reconstruction stencils are used. The accuracy, computational efficiency and performance of the implemented piecewise-linear interface reconstruction methods coupled with different reconstruction stencils are thoroughly analyzed for the reconstruction of interfaces in static conditions and dynamic simulations that produce highly deformed interfaces by using an accurate unsplit geometric advection method and imposing prescribed velocity fields.