Methods for thermochemical convection in Earth’s mantle with force-balanced plates

[1] Models of convection in the mantle can be used to study the effects of differentiation and remixing on the geochemical evolution of the Earth. Implementation of melting and degassing at mid-ocean ridges and subduction zones requires an adequate approximation of plate tectonics as well as temperature-dependent rheology. We have developed a new two-dimensional cylindrical model that combines a force-balance method for energetically consistent stiff plates with tracer-discretized chemical buoyancy. Basaltic crust is extracted at distinct spreading centers and is subducted into the lower mantle. We find that the unmodified implementation of the force-balance equations in a full cylinder causes occasional spurious rotations by amplification of numerical discretization errors. The method is stable if a single internal symmetry boundary condition is used, but this causes artificial pooling of dense crust near the boundary where it is easily disrupted. This results in artificially enhanced remixing of dense crust. We modify the force-balance equations to damp net lateral plate movement. The energetic consistency of this modification is then demonstrated by comparison to a one-plate, single convection cell calculation. With the removal of the symmetry boundary condition a more continuous rate of crustal pooling is observed. This suggests that models with symmetry boundary conditions may overpredict the rate of pooling and remixing of ancient crust.