Modeling thermodynamically consistent phase transitions in multi-component assemblages: An entropy method for geodynamic models

Abstract. Phase transitions strongly influence mantle convection as their effects on buoyancy can hinder or accelerate slabs and plumes. In a heterogeneous mantle, different mineral assemblages undergo phase transitions at different depths, leading to lateral buoyancy variations that can cause specific compositions to stagnate or accumulate within characteristic depth ranges. However, complex phase relations, abrupt changes in material properties, and the release and absorption of latent heat pose significant challenges for modeling phase transitions. Our previous work addressed these challenges by formulating the energy equation in terms of entropy rather than temperature, but remained limited to chemically homogeneous models. Here we extend the entropy formulation to multiple components. By solving one entropy advection equation for each chemical component and then thermally equilibrating all components, our method enables a thermodynamically consistent treatment of phase transitions in multi-component systems. Our tests demonstrate that the method accurately conserves energy, and remains robust even for degenerate cases. We show its applicability in a series of global convection models, which reveal that small differences in phase relations between a pyrolitic equilibrium assemblage and a basalt–harzburgite mechanical mixture with the same composition can lead to major differences in convection patterns. Our results highlight the importance of accurately capturing the full effects of phase transitions in a chemically heterogeneous mantle, and our approach enables new investigations into how planetary interiors evolve.