An efficient operator-split CICSAM scheme for three-dimensional multiphase-flow problems on Cartesian grids

Abstract

Conventional algebraic Volume of Fluid (VOF) schemes utilize a Crank-Nicholson-based unsplit advection framework which is necessary for maintaining second-order accuracy in time as well as to allow extension to arbitrary meshes. However, the unsplit advection approach proves to be a bottleneck to computational performance for CFD solvers opting for non-body-conforming Cartesian grids for treating complex domains and immersed boundaries. To this effect, we propose a general operator-splitting framework for algebraic VOF schemes and develop a direction-split version of the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The resulting operator-split CICSAM (OS-CICSAM) scheme is compared against unsplit CICSAM as well as two recent algebraic VOF schemes for standard advection tests. In terms of volume tracking performance as well as interfacial shape preservation, it is demonstrated that OS-CICSAM attains comparable or lower L1 error norm, has rates of convergence intermediate to first and second order and is at least 600% faster in comparison to unsplit algebraic VOF schemes. The OS-CICSAM scheme is then coupled with the in-house CFD solver IITM-RANS3D. The robustness of the proposed scheme is established by applying to benchmark problems such as Rayleigh-Taylor instability and free surface wave interactions with a structure.