An Efficient Mesh Management for Moving Boundaries Associated with Erosion Events
Ulisses Mello and Ildar Khabibrakhmanov
Research Division, IBM T. J. Watson Research Center, Yorktown Heights, New York
The utilization of unstructured tetrahedral meshes has the potential to allow more realistic modeling of complex geological features present in basin modeling such as fault, salt structures and erosion. However, due the dynamic nature of the evolution of sedimentary basins associated with events like deposition, compaction, salt and fault motion, and erosion, the management of unstructured meshes is more complex than the structured curvilinear grids. Deposition and erosion are part of a class of problems known as moving boundary (or interface) which poses numerical challenges to mesh management, discretization, and computational load balancing. In this presentation, we discuss some strategies to manage the mesh during erosion events and hence minimize the mesh changes during the modeling.
The deposition of sediments is normally modeled by the creation of additional discrete finite elements or control volumes on the moving interface, the top of the basin. The creation of these elements requires the creation of new nodes where, in general, primary variables such as pressure and temperature are calculated. Consequently, the system of equations solved and associated work load varies during the simulation. This variation causes undesirable side effects related to the book-keeping of the node indices in the system of equation and its negative effects on the workload distribution especially in parallel implementations. Erosion causes even more undesirable effects since it can be very localized in a part of the model. Remeshing is a legitimate approach to address the changes in the model geometry in these events. However, automatic remeshing of unstructured tetrahedral meshes sometimes lacks robustness due to the geometrical characteristics of a given model (i.e., very thin layer, nodes too close, etc). In addition, after the remeshing proper conservative projections have to be used to calculate values of the primary variables on the new mesh to avoid loss of mass end energy conservation in the process of transferring the primary variable values. Remeshing, conservative projection, and redistribution of the work load are computationally expensive.
In this presentation, we describe an approach to handle deposition and erosion which minimizes changes in the topology of unstructured meshes and thus no remeshing is necessary during the basin simulation. In this approach, we take into account all the topological changes associated with the deposition and erosion in the mesh generation process. Consequently, mesh used in the modeling has a discretization that is able represent discrete erosion events without remeshing. In this approach we use erosion maps, to reconstruct the geometry and topology of the layer before the deposition and we include the reconstructed horizons as well the present-day horizons to constrain the mesh generation process. This mesh is then segmented spatially and temporally to classify the elements accordingly to the geological events. During the simulation, the elements are added or removed from the simulation based on the classification previously defined.
Therefore, a set of elements may represent a given layer before the erosion and another after a subsequent deposition. Because the mesh configuration for each simulation time interval is known a priori, efficient workload distribution can be devised.
AAPG Search and Discovery Article #90091©2009 AAPG Hedberg Research Conference, May 3-7, 2009 - Napa, California, U.S.A.