Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems

We have extended our previous 2D method [Gerya, T.V., Yuen, D.A., 2003. Characteristics-based marker-in-cell method with conservative finite-differences schemes for modeling geological flows with strongly variable transport properties. Phys. Earth Planet. Interiors 140, 295-320], which is a combination of conservative finite-differences with marker-in-cell techniques to include the effects of visco-elasto-plastic rheology, self-gravitation and a self-consistently derived evolving curvilinear planetary surface. This code is called I2ELVIS and can solve a new class of computationally challenging problems in geodynamics, such as shear localization with large strains, crustal intrusion emplacement of magmas, bending of realistic visco-elasto-plastic plates and core-formation by vigorous shell tectonics activities related to a global Rayleigh-Taylor instability of a metal layer formed around silicate-rich lower density (primordial) core during planetary accretion. We discuss in detail the computational strategy required the rheological constraints to be satisfied at each time step and spatial location. We show analytical benchmarks and examples drawn from comparing between numerical and analogue experiments in structural geology, subducting slab bending with a visco-elasto-plastic rheology and equilibrium spherical configurations from self-gravitation. We have also tested possibilities of future applications by addressing 3D geometries based on multigrid method and including inertial effects in the momentum equation with tracers in order to simulate meteoritic impact events and eventually earthquake instabilities.