A new interface‐capturing discretization scheme for numerical solution of the volume fraction equation in two‐phase flows

Abstract

AbstractA new high‐resolution spatial discretization scheme for use with the interface‐capturing volume‐of‐fluid method is presented and applied to several test cases. The new scheme is intended to preserve the volume fraction discontinuity without the need to explicitly reconstruct the interface within computational control volumes 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 computational control volume. In addition, the scheme employs face limiting to satisfy 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 flow fields. 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 test cases, and is shown to preserve the phase interface almost exactly, with essentially zero dissipative or dispersive error in the volume fraction solution. Copyright © 2008 John Wiley & Sons, Ltd.