An Improved High-Resolution Discretization Scheme for Volume-of-Fluid CFD Simulations

A new high-resolution spatial discretization scheme for use with the interface capturing volume-of-fluid (VOF) method is presented and applied to several test cases. The new scheme is shown to preserve the volume fraction discontinuity within a single computational control volume (CV), without the need to explicitly reconstruct the interface within CVs near the interface. The method is based on maximization of the volume fraction gradient in the region of the interface, while stability is preserved by maintaining net upwind biasing of the face flux prescription in each CV. In addition, the scheme employs face limiting to satisfy physical boundedness criteria at finite-volume control surfaces (faces) and prevent variable overshoot. The method has been developed for use with unstructured, anisotropic, and/or inhomogeneous meshes that are often used for simulation of geometrically complex flowfields. This paper presents the implementation of the new discretization scheme into a steady-state solver in order to isolate the spatial discretization from the time integration technique. The new scheme is validated for steady-state two-phase flow using several demonstration test cases, and is shown to preserve the phase interface almost exactly, with essentially zero dissipative or dispersive error in the volume fraction solution. Results are compared to existing 2nd order and high-resolution interface capturing (HRIC) schemes, and shown to be superior in all cases.