Parallel numerical reservoir simulation: A feasibility study

This paper discusses a feasibility study to implement a parallel reservoir simulator on parallel computers. The basis of-this study is a reservoir simulator that models an injectionproduction mechanism. The simulator implements a multigrid solver for the elliptic part of the equations, and uses adaptive local grid refinement to track moving fronts in the reservoir. The parallelization method is based on a domain decomposition method, which assigns the subdomains to the processors. In order to obtain a correct solution, communication across the internal boundaries between the subdomains is required. The implementation of the multigrid method imposes restrictions on the domain decomposition. Furthermore, the adaptive local grid refinement may cause the work load distribution over the processors to be out of balance. Hence, some load balancing technique is required to ensure parallel efficiency. This parallel &efficiency is illustrated by experiments on a Convex MetaSeries system. Since the number of processors is small with respect to the problem size, it seems natural to apply a domain decomposition technique to the computational domain. In practice, this means that a typical grid as shown in figure 1 is split into a number of subdomains, which will be assigned to the processors of the parallel computer. Note that the number of subdomains not necessarily equals the number of processors. The decomposition introduces internal boundaries between the subdomains. Across these boundaries, communication between the subdomains is necessary in order to obtain a correct solution. An example of domain decomposition on the grid of figure 1 is shown in figure 2.