Multiphase Lagrangian Differencing Dynamics method with sharp interfaces

Abstract

Multiphase flow simulations are complex due to the intricate interactions between phases when high density and viscosity ratios are involved. These complexities often lead to challenges in capturing sharp interfaces and managing pressure jumps across phases, which can induce numerical instability. Extending the Lagrangian Differencing Dynamics (LDD) method which differs from other meshless methods by using a unique approximation scheme that ensures accurate gradients and Laplacians with second-order consistency, prioritizing consistency over traditional conservation-first approaches and also works directly on the surface meshes. This paper presents a novel Multiphase Lagrangian Differencing Dynamics (MP-LDD) with a sharp interface without density and viscosity diffusion at the interface. The method incorporates several key techniques to address the challenges: introduced a second-order consistency variable coefficient Laplacian operator for discretizing pressure and velocity equations to handle varying densities and viscosities; a systematic approach to point-cloud regularization using Position Based Dynamics (PBD) for the multiphase framework that integrates the Atwood number and increase/decrease of density to ensure a sharp and stable interface, for simulating flows with high-density ratios and mitigating unintended mixing between immiscible fluids at the interface. The Lagrangian CFL criterion is also employed for automatic time-stepping, facilitating larger time steps and accelerating simulations while maintaining numerical stability. The effectiveness of the MP-LDD approach is demonstrated through validation against various benchmark cases, including 2D Rayleigh–Taylor instability for low-density ratio, dam break & sloshing for high-density ratio & violent flows. Also, oil injection into the water scenario showcases high-density and viscosity fluids.