Thermal Lattice Boltzmann Modeling of Archean Continent Formation Using a Rothman–Keller Multiphase Framework

The formation and stabilization of continental crust during the Archean remains a fundamental problem in Earth sciences, requiring numerical models that can self-consistently capture multiphase flow, melt segregation, and thermochemical buoyancy within a convecting mantle. Here, we employ a thermal Lattice Boltzmann Method (TLBM) based on the Rothman–Keller multiphase formulation to investigate continent formation in a dynamically evolving Archean mantle. The model resolves two interacting lithological components representing basaltic crust and peridotitic mantle, coupled to a thermal field through the Boussinesq approximation. Melt generation, extraction, and retention are explicitly incorporated, allowing density and viscosity to evolve continuously as functions of temperature, melt fraction, and composition. Melt extracted from basalt is treated as an immiscible, low-density phase representing Tonalite–Trondhjemite–Granodiorite (TTG) crust. Unlike traditional marker-based or fixed-density approaches, this framework enables self-consistent tracking of compositional evolution without prescribing rigid phase boundaries. Simulations are conducted in annular geometry to approximate spherical curvature while retaining computational efficiency, with spatial resolution ranging from ∼15 km near the surface to ∼8 km at the core–mantle boundary (CMB). Results show that thermally driven melt production and compositional differentiation naturally generate buoyant, long-lived TTG crust that thickens and stabilizes against recycling. Residual basalt forms a denser layer beneath the TTG crust, contributing to lithospheric stabilization while remaining susceptible to recycling under cold, dense conditions.