Faccenda et al. (2012) suggested new explanation for DSZs based  on numerical models of a dynamically subducting and dehydrating oceanic plate. Results show that, during slab dehydration, unbending stresses drive part of the released fluids into the cold core of the plate toward a level of strong tectonic under-pressure and neutral (slab-normal) pressure gradients. Fluids progressively accumulate and percolate updip along such a layer forming, together with the upper hydrated layer near the top of the slab, a Double Hydrated Zone (DHZ) where intermediate-depth seismicity could be triggered.

Cramery et al. (2012) presented first self-consistent 3D numerical models of global mantle convection with asymmetric (one-sided) subduction and curved trenches. The asymmetry of subduction results from two major features of terrestrial plates that were not previously implemented in global models: (1) the presence of a free deformable upper surface and (2) the presence of weak hydrated crust atop sub ducting slabs.

I recently noticed that I almost stopped to store raw data coming from my numerical experiments. Instead, I document the experiments with series of informative pictures and delete the majority of the raw data. The reason is that even with a reasonable reduction each numerical experiment requires 200-500 GB storage for the raw data. Running tens of experiments every month produces so much data that it is not reasonable to store them all (especially when any experiment can be re-run within a few days time). Obviously, this strategy can only work if there is little/no limitation for computer power and the explored numerical codes run reasonably fast…

A review of origin and models of transform faults discusses key natural data and numerical and analogue modeling results for these enigmatic structures. Models of transform faults are yet relatively scarce and partly controversial. Consequently, a number of first order questions remain standing and significant cross-disciplinary efforts are needed in the future by combining natural observations, analogue experiments, and numerical modeling.

Depending on which type of boundary condition is used, the FD-MIC scheme is a second order accurate in space as long as the viscosity field is constant or smooth (i.e. continuous). With the introduction of a discontinuous viscosity field characterized by a viscosity jump within the control volume, the scheme becomes first order accurate. The transition from second order to first order accuracy will occur with only a small increase in the viscosity contrast of around five.

A review of subduction models highlights a number of open topics for the future research:

Resolving the controversy of subduction initiation.

Constraining robust high-resolution models of terrestrial plate tectonics.

Understanding deep slab processes in the mantle.

Constraining crustal growth and differentiation in magmatic arcs.

Modeling of fluid and melt transport in subduction zones.

Deciphering evolution of high- and ultrahigh-pressure rock complexes.

Developing geochemical-thermo-mechanical models of subduction.

Coupling of subduction models with volcanic and seismic risk assessment.

Understanding the onset of plate tectonics on Earth.

Boris Kaus and David May compared the relative performance of the FDM versus the FEM for a few selected benchmark cases. They found that under conditions of high viscosity and density contrasts many of commonly used finite elements (such as Q1P0 and stabilized Q1Q1) often produce numerical artifacts when viscosity and density boundaries are crossing boundaries of elements. In contrast, finite differences on staggered grid always behave as most stable finite elements (such as or Q2P-1) but require 12 time less computational power.

Thibault Duretz and co-workers studied the accuracy of the finite difference and marker-in-cell technique for the discretization of Stokes equations in two dimensions. They examined the convergence properties of the traditional staggered grid discretization and showed that introducing an interpolated viscosity constructed from the markers does not modify the convergence behavior. They also proposed a stabilization algorithm for free surface which is suitable for finite difference methods.

Large group of modelers examined various implementations of free surface for geodynamic problems. They evaluated two cases that characterize the evolution of topography on different timescales: (1) relaxation of a sinusoidal perturbation and (2) topography changes above a rising sphere.  It is found that the sticky air approach works fine as long as free surface quality term is small that mainly depends on the thickness of the sticky air layer and the viscosity contrast between this layer and the characteristic viscosity of the model. For typical geodynamic applications thickness and viscosity of the sticky air should be on the order of n*10 km and n*1e+17 Pa s, respectively.

Yury Mishin and co-workers presented an adaptive multi-resolution method (AMR) based on finite elements for solving problems of computational geodynamics. It was demonstrated that the use of expensive higher order stable elements (such as or Q2P-1) in combination with adaptive grid refinement become computationally efficient strategy that allows for up 1000 time speed up of numerical solutions without losing its accuracy compared to uniformly resolved grids of the highest resolution. Thus, this method can efficiently compete with finite differences on staggered grid for applications where various localization phenomena are modeled.

Indeed, similar AMR approach can also be constructed with the use of stress-conservative finite differences and staggered grid. Compared to uniform staggered grid of the same effective resolution, computational costs in 2D typically decrease as 2^N, where N is the number of resolution levels.

Earth is a complex object whose interior evolves on geological timescales that are inaccessible for direct observation. Therefore, understanding of Earth’s dynamics unavoidably involves a lot of scientific intuition that should be assisted by modeling. In a way, modeling serves us as a tool to develop intuition for very deep and very slow geological processes that are out of our every-day experience. Consequently the use of numerical modeling is crucial for geodynamics and its role will only grow in the future to develop, test and quantify hypotheses.

Spontaneous subduction initiation may have a hidden initial phase that is not expressed in diagnostic features such as trench and magmatic arc. Ksenia Nikolaeva and co-workers analyzed numerically the probability of subduction initiation along the Atlantic American passive margins based on their topography and lithospheric and crustal structure. According to the experimental results, proper subduction will likely start during the next 10–20 m.y. along the southern part of the Brazilian margin, while other Atlantic margins of North and South America are stable under the present geodynamic conditions.

It is often assumed that obtaining a good thermo-mechanical code guarantees success in numerical geodynamic modeling. Thinking that is a “big mistake”! Writing an extremely reliable code DOES NOT automatically implies that you will be successful as a modeler… We have to learn how to use our codes in the most efficient way, how to construct robust numerical models of various geodynamic and planetary processes, how to visualize and investigate these models and how to compare them to nature. In short: designing thoughtful and realistic numerical models, finding robust initial and boundary conditions are at least as important as writing efficient numerical codes.