2.6 Initial conditions and the adiabatic pressure/temperature

Equations (1)–(3) require us to pose initial conditions for the temperature, and this is done by selecting one of the existing models for initial conditions in the input parameter file, see Section ??. The equations themselves do not require that initial conditions are specified for the velocity and pressure variables (since there are no time derivatives on these variables in the model).

Nevertheless, a nonlinear solver will have difficulty converging to the correct solution if we start with a completely unphysical pressure for models in which coefficients such as density $\rho$ and viscosity $\eta$ depend on the pressure and temperature. To this end, ASPECT uses pressure and temperature fields $p_{\mathrm{\text{ad}}}\left(z\right),T_{\mathrm{\text{ad}}}\left(z\right)$ computed in the adiabatic conditions model (see Section ??). By default, these fields satisfy adiabatic conditions:

where strictly speaking $g_z$ is the magnitude of the vertical component of the gravity vector field, but in practice we take the magnitude of the entire gravity vector.

These equations can be integrated numerically starting at $z=0$, using the depth dependent gravity field and values of the coefficients $\rho =\rho \left(p,T,z\right),C_p=C_p\left(p,T,z\right)$. As starting conditions at $z=0$ we choose a pressure $p_{\mathrm{\text{ad}}}\left(0\right)$ equal to the average surface pressure (often chosen to be zero, see Section 2.5), and an adiabatic surface temperature $T_{\mathrm{\text{ad}}}\left(0\right)$ that is also selected in the input parameter file.

However, users can also supply their own adiabatic conditions models or define an arbitrary profile using the “function” plugin.