Apparatus, method and system for improved reservoir simulation using an algebraic cascading class linear solver

Abstract

A method, system, a program storage device and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a region of interest, wherein the region of interest has been gridded into cells. Each cell has one or more unknown variable. Each cell has a node. A graph of the nodes is represented by a sparse matrix. The graph is an initially decomposed into a pre-specified number of domains, such that each cell exists in at least one domain. The cells and domains are numbered. Each cell has a key, the key of each cell is the set of domain numbers to which the cell belongs. Each cell has a class, the class of each cell being the number of elements in the cell. The cells are grouped into connectors, each connector being the set of cells that share the same key. Each connector having a connector class, the connector class being the number of elements in the key of the connector. Each connector having only one higher-order neighbor connector is merged with such higher-order neighbor connector. The class of all locally maximum class connectors is reset to the maximum class of held by any connector. The maximum class connector is forced to contain only one cell. The connectors are ordered in increasing order of class. Interpolation operator and restriction operator are constructed from the ordered connectors. The interpolation operator and restriction operator are used to construct a coarse grid. The coarse grid may be used to determine the unknown variables of the cells.