Performance analysis and reconstruction of interface capturing schemes for multiphase flows

This article aims to provide a roadmap for analysis of the interface capturing schemes and their possible modification with recommended design principles. Blending the suitable high resolution (HR) scheme with a bounded downwind (BD) scheme is the core of the development of any interface capturing scheme. However, the concrete guidelines for choice of HR and BD schemes are not clear. For this purpose, the HR and BD constituents of a popular scheme known as "Switching Technique for Advection and Capturing of Surfaces (STACS)" are analyzed. Subsequently, it is observed that the scheme fails to satisfy some critical design principles. This leads to a reconstruction of the scheme by introducing a newly compliant bounded downwind scheme. The novel re-constructed scheme is then accessed through typical advection problems, including the shear flow on structured and unstructured meshes. The scheme convincingly outperforms its parent scheme in all test cases irrespective of the Courant number. Moreover, it generates superior or at least at par results while compared with a few well-established schemes like Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) and Cubic Upwind Interpolation based Blending Scheme (CUIBS).