Numerical Enhancements to the Model Sample Clauses

Numerical Enhancements to the Model. We present a summary of the local grid-refinement method and implementation in UTCHEM. The formulation and simulation examples are given in UTCHEM-LGR User's manual. The aquifer is initially defined by a coarse grid (called a base grid) with NXCxNYCxNZC standard cells (gridblocks). Subject to memory limitations, any number and any combination of the base grid cells can be refined by a single local-level NXFxNYFxNZF that is of fixed resolution for all refined cells. The refined base grid cells are called zones. The resulting grid is comprised of coarse base cells and fine-zone regions. When a coarse base cell or a fine zone is adjacent to a refined base cell or zone, this gives rise to a coarse-fine interface or fine-fine interface, respectively. With respect to a given zone, the interfaces act as interior domain boundaries. An example is presented in Fig. 1.2, where the definition of zone and interface are illustrated in Fig. 1.2a. The implementation strategy attempts to treat each zone as a separate domain subject to interior domain boundary conditions and is in that sense based on domain decomposition, pictorially illustrated in Fig. 1.2b. Computations in the interior of each local fine zone are effectively performed in isolation from other regions of the flow domain (giving rise to an inner loop) subject to appropriate interface and exterior boundary conditions that are imposed in an outer loop over the local domains and serve to connect the various local domains together. Local grid refinement (LGR) has been implemented for the Cartesian option with a higher-order scheme or two-point upstream weighting for the concentration equations, although single-point upstream weighting is also maintained as an option. While the current code allows static (fixed) local cell refinement, where each coarse cell selected for refinement remains refined and the grid does not change throughout the computation, the implementation will allow future extension to dynamic local refinement. Some recent examples of use of this kind of local refinement in reservoir simulation can be found in Espedal et al. [1990] and Xxxxxxxxxx and Heinemann [1993]. However, with the exception of Xxxxxxx [1992a,b] and Xxxxxxx and Xxxxxxxx [1993] where a higher-order (in space and time) total-variation-diminishing type scheme is employed, all other adaptive methods in reservoir simulation to date have employed first-order upstream differencing for discretization of the advective terms in the flow...
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