An Extended Full GKS Formulation for High-Efficiency and Low-Memory Two-Phase Flow Simulation

Two-phase flows are ubiquitous in nature, exhibiting complex fluid-fluid interactions that challenges numerical simulators. To accurately and efficiently solve two-phase flows, grid-based methods have been widely adopted. Navier-Stokes (NS) solvers consume a small memory footprint, but simultaneously achieving both high performance and low numerical dissipation remains a significant challenge. In contrast, lattice Boltzmann solvers are efficient and have low numerical dissipation, yet they remain memoryintensive, even with state-of-the-art moment-encoding schemes. To date, the simultaneous attainment of high accuracy, exceptional efficiency, and a low memory footprint remains a major challenge in the field. In this paper, we propose a novel two-phase flow solver that achieves this objective. Our work is motivated by extending gas-kinetic scheme (GKS), which is adapted to handle nearly incompressible flows. To allow stable and accurate two-phase flow simulations, we systematically derive a coupled formulation of the GKS method and the phase-field model, incorporating novel mathematical constructs. Combined with robust boundary treatments and specialized techniques for handling turbulent flows, this results a unified framework capable of efficiently simulating two-phase flows, even those with large density contrasts and high Reynolds numbers. Since our formulation is explicit, it achieves exceptional performance when optimized on GPU, making it the fastest kinetic two-phase flow solver to date. Additionally, as it is derived from GKS, it obviates the need to store distribution functions. Thus, it has a small memory footprint, competitive with, or even lower than, that of many NS solvers. As a result, our solver can efficiently simulate complex two-phase flow dynamics at high resolutions using a single commodity GPU. We validate the accuracy of our solver via several benchmark tests, compare its performance with recent methods in various aspects, and demonstrate its capability to replicate a broad range of two-phase flow phenomena, encompassing both typical and large-scale scenarios.