Geodynamics Modelling Through Coupling Abaqus with an Accelerated Boundary Element Method
(2006) 1st International Geoscientific Abaqus Workshop 2006 — Location: Ruhr-University Bochum, Bochum, Germany (4.October.2006)
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- Abstract
- Geodynamical numerical models usually have to deal with large viscosity variations in relatively small domains, occurring from the crustal up to the planetary scale. Furthermore relevant geophysical events are often located only within a small portion of the Earth (e.g. earthquakes at plate boundaries and within the core of subducting slabs, exhumation and volcanism at back-arc areas). It is therefore highly desirable to model separately at high resolution the zone interesting for the modeller, preserving the self consistent feed-back with the background dynamics. In this lecture a hybrid approach is presented for coupling solid and fluid within the Stokes flow approximation (negligible inertia). The technique combines Fast Multipole BEM and Lagrangian Mechanical FEM (Abaqus implicit): the first calculates the drag due to Stokes flow in bounded and unbounded domains, the second solves the fine and eventually complex thermo-mechanical dynamics of the area of interest. Tests are performed for large strain 3-D Rayleigh Taylor Instability in a box and viscosity variations of several orders of magnitude, for a rising plume in the mantle and for modelling first order interaction between close and far subduction systems. In general the evolving boundary between a solid and a fluid is characterized by a discontinuity in stress (e.g. due to viscosity change or visco to visco-elastic transition), but continuity in velocity. Coupling FEM and the BEM allow reproducing such interaction after the choice of the proper strategy for exchanging both velocity and stress between the two domains. Coupling modality on the domains boundary can be either implicit or explicit and includes velocity, stress or both. In this lecture a specific innovative technique based on "drag tensors" for the stress-velocity feedback is proposed and explained in details, showing advantages and limitations, through several examples and verification tests. Validation benchmarks show that the method is especially suitable for very large viscosity variations at the BEM-FEM boundary. Performances tests indicate that the BEM solver scales linearly with the problem size, O(N), while the FEM scales between O(N*sqrt(N)) and O(N^2), where N is the number of elements. The integration of the method in Abaqus is done employing the external subroutines DLOAD and UTRACLOAD for imposing the adaptive drag tensors and the routine URDFIL for extracting and elaborating the results at each increment and for calling the external BEM code. The implementation is based on coupling brick type Finite Elements with triangular Boundary Elements. The local drag tensors at each element side are passed from URDFIL to UTRACLOAD through commonly allocated arrays. The entire implementation is pre-processed using a python script that creates the combined BEM and FEM meshes, the input files for Abaqus, the one for the BEM code and takes care of the staggered model evolution. Some didactical examples of subroutines will be available for download.
- Affiliations
ETH Zurich Institute of Geophysics and Computational Laboratory
Citations
Morra, G., & Chatelain, P. (2006). Geodynamics Modelling Through Coupling Abaqus with an Accelerated Boundary Element Method. 1st International Geoscientific Abaqus Workshop 2006, Ruhr-University Bochum, Bochum, Germany. https://hdl.handle.net/2078.5/179536