Domain decomposition and Schur complement approaches to coupling the well equations in reservoir simulation

This note reports on the construction of preconditionings for bordered systems arising in compositional hydrocarbon reservoir modeling. The main portion of the system represents the reservoir equations, and the borders of the systems are associated with the production or injection constraints imposed on the active wells of the reservoir being modeled. In general, the simulation studies are sensitive to the accuracy of the solution at the wells. This note describes strategies for extending a reservoir preconditioning to the well terms. Three alternatives are considered including borrowing ideas from domain decomposition with one domain being the reservoir and the other domain being the well terms. The preconditioners were applied to several linear systems generated by a compositional reservoir simulator, which included various choices for the number of oil wells. The preconditioned iterative methods considered are MINRES and Bi-CGSTAB, which are variants of the conjugate gradient method. This note also rep...