Multiblock Methods for Unstructured Grids in Reservoir Simulation

Unstructured grids are characterized by a variable number of neighborhood relationships between single grid cells. These grids are highly suitable to model the complex geological features of hydrocarbon reservoirs, as for example faults or pinch-outs, in high detail. The application of unstructured grids in reservoir simulation is still very limited, despite the increased quality of the calculated results, as the resulting linear equation systems necessitate special preconditioning methods and solvers, that strongly increase CPU time. Although these grids are globally unstructured, i.e. there is no logical neighborhood ordering for the full simulation model, one can still identify patches in which the grid is locally structured. The Multiblock method can be used to decompose the grid into subdomains (blocks), and to solve each of these blocks separately, connecting neighboring blocks only via boundary conditions. This method can be employed to decompose unstructured grids into single structured blocks and to take advantage of the fixed number of neighborhood relationships in order to simplify and accelerate the solution procedure. Further acceleration can be achieved by the straight forward parallelization of this technique. Objective of this research project is to extend the applicability of the multiblock approach to its application to unstructured grids in reservoir simulation, with focus on unstructured Voronoi grids, as well as the formulation of guidelines that make unstructured grids more efficient in their practical application. New methods for decomposing grids and solving the resulting linear equation system will be developed and algorithmic formulations for their application on parallel computers elaborated.