A general sharp-interface simulation framework for microstructure evolution

Simulating microstructure evolution requires tracking many moving grain and phase boundaries coupled to thermodynamic and mechanical fields. We present Gaussian-projected kinetics (GPK), a sharp-interface framework in which every cell stores an integer grain or phase label. Near a boundary, a temporary Gaussian projection of the label map provides the interface normal and curvature and is then discarded. Capillarity, chemistry, stored energy, transport and elasticity move the boundaries through one topology-preserving update. Because the Gaussian measurement length is fixed in physical units, mesh refinement keeps a consistent capillary scale without a diffuse interface. GPK models grain growth, recrystallisation, multiphase evolution and elastic-coupled solidification in two and three dimensions. It is verified on analytical benchmarks and compared grain by grain with phase-field simulations, running 8.5 to 96 times faster at matched accuracy in our tests. An Al-Cu application with CALPHAD thermodynamic data connects it to measured recrystallisation and precipitation data.