Thermal modeling using finite difference methods is widely used to simulate geologic processes. Methods must simulate the transfer of heat by conduction and advection (movement of material). Simulation of some advective processes, such as faulting, produce discontinuities in the arrays of physical constants; however, most finite difference treatments of advection yield unacceptable levels of diffusion (dissipation or smearing) or dispersion (oscillations) in the neighborhood of discontinuities. A high-resolution finite difference algorithm (flux-corrected transport) that successfully treats advection in arrays containing discontinuities, designed for modeling incompressible non-divergent fluid flow and originally intended for atmospheric applications, may be applied to solid earth problems. Relatively small features or heterogeneities defined within the physical constant arrays remain well resolved throughout the runs as they migrate or deform according to the motion specified in the vector arrays. Thermal modeling may be performed by alternating advection steps, as described, with heat conduction steps, performed in this case with the implicit alternating direction method.

A Windows-based program incorporating these methods, THERMOD8, is available for download at http://jan.ucc.nau.edu/~tdh5/thermod.htm. A user-friendly graphical user interface simplifies the process of specifying models and a tutorial provides instruction and examples. Users may specify 1-d or 2-d models of just advection, just heat conduction, or heat conduction plus advection. Models may involve the crystallization of melts. A choice of boundary conditions is provided. When the automated 2-d fault setup module is used, pressure-temperature-time (PTt) paths may be calculated for points in the system. Faults are specified by entering geometric and distance parameters and the slip rate, positive for normal-sense movement and negative for reverse. Exhumation or burial at uniform rates may also be incorporated. The results from any chosen time step in one simulation may be used as starting conditions for another different simulation, allowing complex scenarios to be simulated. Simulations permit interpretations of thermochronologic data and metamorphic PTt paths to be tested.