APPARATUS, METHOD AND SYSTEM FOR RESERVOIR SIMULATION USING A MULTIPLICATIVE OVERLAPPING SCHWARZ PRECONDITIONING FOR ADAPTIVE IMPLICIT LINEAR SYSTEMS

摘要

A method, system and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a gridded region of interest. The grid of the region of interest includes one or more types of cells, the type of cell being distinguished by the number of unknown variables representing properties of the cells. The cells share a common variable as an unknown variable. The method includes the steps of identifying different cell types for the grid; constructing an overall matrix for the reservoir model based on the different cell types; at least partially decoupling the common variable from the other unknown variables in the matrix by using a reduction process to yield a reduced matrix; mathematically breaking up the variables in the reduced matrix into k subsets by cell types; applying an overlapping multiplicative Schwartz procedure to the reduced matrix to obtain a preconditioner and using the preconditioner to solve for the unknown variables.