Gcube, a new three-dimensional model of lithospheric deformation and mantle flow
J. Braun, P. Fullsack & M. DeKool
In the last 12 months, we have developed a new finite element code, which we called Gcube, to solve the equations of quasi-static force force balance in three dimensions that will allow us to simulate the deformation of the lithosphere and its coupling to flow in the underlying mantle. Of particular interest to us is the strong interactions between the solid lithosphere and the hydrosphere through the process of erosion, transport and sedimentation.
The method differs from classical finite element based approaches in several aspects
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it allows for the accurate tracking of the free surface, internal boundaries and clouds of points on which the history of the flow can be stored; this is achieved by using a combination of particle-based methods and level set functions;
it is based on a non-uniform, yet regular discretization of three-dimensional space through the use of an octree structure; octrees are also used to communicate information between the finite elements and the tracked interfaces;
the solution of the large system of algebraic equations is performed by a parallelized version of a direct Cholesky solver developed by the IBM Watson Labs.
So far, predictions of the model have been tested against the results of laboratory experiments in which a solid body (a pétanque ball) is slowly sinking in a highly viscous silicon oil, deforming the surface of the fluid. The comparison demonstrated the accuracy and efficiency of the method.
Figure 3: (a) Results of the laboratory experiment after the pétanque ball has sunk to a depth approximately equal to its own diameter. (b) Numerical simulation using Gcube in which the ball has sunk to a depth greater than twice its diameter.