ShanghaiTech University
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 memory-intensive, 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.
Coastal wave dynamics
Ocean waves advance toward a rocky shore and break against the rocks, producing splashes and turbulent water motion. The flow spreads around the shoreline geometry as successive waves arrive, creating interacting currents and continually reshaping the water surface.
Buoyancy-driven mixing
A denser fluid initially lies above a lighter fluid. A descending spike and interfacial shear vortices develop as the instability grows. The denser phase sinks while the lighter phase rises, eventually approaching a stably stratified equilibrium.
Capillary contraction and breakup
An initially stationary water torus contracts under surface tension in zero gravity, forming a nearly spherical shape before elongating into a liquid rod. The rod subsequently breaks into separate droplets through the Plateau–Rayleigh instability.
Surface wettability
Water impinges on hydrophilic and hydrophobic spheres. On the hydrophilic surface, it spreads into a smooth film and detaches farther down. On the hydrophobic surface, weaker adhesion produces a less continuous flow that detaches higher up.
Air-water exchange
Water drains from an inverted bottle while incoming air rises as bubbles. The small initial air headspace produces rapid pressure fluctuations and frequent glugging. As more air enters, the glugging frequency decreases slightly while the bottle continues to drain.
Pressure-driven siphoning
Water gradually fills a Pythagoras cup until its level exceeds the crest of the internal tube, initiating a siphon. After the inlet closes, water continues flowing through the tube into the reservoir below until the cup is nearly empty.
Flow in complex porous media
Water injected from above follows branching paths through a porous medium under gravity. As it descends, the flow spreads through interconnected pores. After the inlet closes, the remaining water drains through these channels and collects in a puddle below.
Large-scale hydraulic flow
A continuous inflow maintains the reservoir level upstream of a piano key weir. The upstream water surface remains relatively calm, while water accelerates over the structure. The overflowing streams enter the downstream channel, where they form turbulent flow.
Transient wave impact
A large wave strikes an arched iron bridge and surges through its steel framework. The impact produces fragmented splashes around the structure. Water then propagates downstream as churning waves, leaving a turbulent flow in the wake of the impact.