An enhanced un-split face-vertex flux-based VoF method

Abstract

Multiple advancements of the dimensionally un-split, flux-based geometrical Volume-of-Fluid method on unstructured meshes are proposed. A second-order accurate interface reconstruction algorithm for both two-and-three dimensions is developed on unstructured hexahedral meshes. A new triangulation algorithm is developed that results in an absolute increase in accuracy and can be directly applied to other geometrical Volume-of-Fluid methods on both structured and unstructured meshes. A second-order accurate interpolation of point displacements is proposed for unstructured meshes. A global parallel error re-distribution algorithm is developed, with no negative effects on the L1 error convergence and computational costs. All algorithms are parallelized using the message passing parallel programming model, with a minimal parallel communication overhead. The results show L1 errors to be exactly numerically bounded, second-order convergent and lower than the errors reported for other contemporary methods, volume conservation that is near machine tolerance, as well as execution times comparable to those of methods developed on structured Cartesian meshes, regardless of the increased algorithmic complexity introduced by the connectivity of unstructured meshes.