A Fully Conservative Scheme for Simulating Turbulent Incompressible Multiphase Flows

Accurate simulation of multiphase flows with evolving interface topologies remains a central challenge in computational fluid dynamics. The physical fidelity of such simulations critically depends on the numerical scheme's ability to conserve fundamental quantities such as mass, momentum, and kinetic energy. While many existing methods preserve some of these properties, achieving simultaneous conservation of all has remained elusive. In this work, we introduce the first numerical scheme for two-phase incompressible flows that guarantees exact, discrete conservation of phasic volume, mass, momentum, and kinetic energy. Our approach combines a geometric volume-of-fluid (VOF) interface-capturing method with a kinetic-energy-conserving formulation of the governing equations, enabling robust, high-fidelity simulations of complex multiphase flows. We demonstrate the benefits of kinetic energy conservation through test cases including a falling droplet impacting a liquid pool and a liquid jet in a high-speed gas co-flow. Enforcing kinetic energy conservation leads to markedly different and more physically accurate flow behavior compared to non-conservative schemes. These improvements are achieved without additional computational cost, offering a robust and efficient tool for studying turbulence and interfacial dynamics across a wide range of applications.