Jeremy Kozdon
Geophysics Department
Stanford University
Stanford, California, USA
Earthquakes pose a huge societal hazard in many parts of the world. The
largest and most destructive events are extremely rare so computation is a
critical partner to theory, experiments, and field work. As computing power
has increased there has been a push to include more realistic physics in the
models. Since earthquakes involve a complex coupling of many different
physical processes at different spatial and temporal-scales this has lead to
many new (and exciting!) numerical challenges.
Our group is tackling these problems through a variety of computational
techniques. The workhorse code of group is based on summation-by-parts
finite difference methods with interface and boundary conditions handled
through the simultaneous approximation term method. Complex geometries are
handled through the use of multiblock grids and coordinate transforms. We
are currently extending this method to handle additional physics (such as
coupling with volcanic conduit flow models) as well as implicit time
integration for quasi-static elasticity so that 10,000 year histories of
repeated earthquakes occurring in response to slow tectonic loading can be
accommodated.
A big challenge in earthquake simulations is the multi-scale nature of the problem. When laboratory measured parameters are used the grid resolution required for accurate simulation is impractically small for fixed grid methods, thus in practice artificially enhanced parameters are used. To explore what is lost by not using laboratory parameters in field-scale simulations, we are developing an adaptive mesh refinement (AMR) code. The numerical method used in the AMR code is a multi-dimensional finite volume method with the Berger-Oliger adaptive time stepping routine.