Article: Owkes, M; Desjardins, O; “A Mass and Momentum Conserving Unsplit Semi-Lagrangian Framework for Simulating Multiphase Flows”, Journal of Computational Physics, 332: 21-46
Abstract: In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas-liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet. (C) 2016 Elsevier Inc. All rights reserved.
Funding Acknowledgement: Advanced Simulation and Computing Program; Scientific Discovery through Advanced Computing Program 
Funding Text: Visualizations in this article were created using the Visit visualizing and analysis tool. Visit is supported by the Department of Energy with funding from the Advanced Simulation and Computing Program and the Scientific Discovery through Advanced Computing Program .