What do we expect from geodynamic codes?

Before describing possible structures for thermomechanical codes, let us discuss what we actually expect from a state-of-the-art, numerical geodynamic modelling tool. Today, as numerical modelling of geodynamic and planetary processes is in the ‘new millennium’ (although it is only around 40 years old, see Introduction), geoscientists are targeting modelling of realistic situations in lithospheric, mantle and planetary dynamics (e.g. Gerya and Yuen, 2007; Moresi et al., 2008; Zhong et al., 2007; Tackley, 2008). The rheology of crustal and mantle rocks depends strongly on the temperature, strain-rate, volatile content, grain size and the fluid pressure. Physical and dynamical circumstances imposed by the sharply varying viscosity represent a major challenge for solving the momentum equation in geodynamics, unlike those found in the oceanographic or atmospheric sciences. Another complication is due to the variable thermal conductivity in the heat conservation equation. The thermal conductivity of various crustal and mantle rocks is notably different and is also a strong function of temperature, pressure and mineralogy which causes numerical difficulties compared to the constant thermal conductivity situation. Finally, all physical (transport) properties of rocks, including viscosity and conductivity, vary strongly with chemical composition and/or mineralogy.