Novel approaches to Two-Fluid models using Lattice Boltzmann method

Mixing in industrial multiphase systems is commonly modelled using the Two-Fluid (TF) model, an Euler–Euler framework that treats each phase as an interpenetrating continuum coupled through interfacial exchange terms. It enables simulation of stirred tanks, bubble columns, and emulsions at practical scales where interface-resolved approaches are infeasible. However, conventional Navier–Stokes–based discretisations can face stability and scalability challenges. The Lattice Boltzmann (LB) method, with its natural parallelism, offers an attractive alternative. Yet robust and general TF implementations within LB remain limited. Here, we propose two novel LB-based formulations of the TF equations. The primary challenge in realising the TF equations in LB is obtaining the correct pressure term. In the first approach, the built-in pressure term in LB is removed using the well-balanced formulation of LB, and the correct pressure term is subsequently reintroduced using a pressure Poisson equation. This reproduces the full TF equations, albeit with the addition of an expensive Poisson equation. The second approach reformulates the TF equations into a mixture equation and a phase momentum equation with correction terms, assuming an incompressible dilute mixture. This approach provides a more efficient, but approximate alternative. The two proposed models are validated against multiple benchmarks and shown to be accurate within their assumptions. Subsequently, they are used in a large eddy simulation to simulate homogeneous isotropic turbulence using the static Smagorinsky model, and the results are validated against a full direct numerical simulation, showing the stability of the proposed models in highly complex and chaotic flows.