Patent ID: 8903694

Claim:
A computer-implemented method for solving linear systems of equations arising in reservoir simulation, the method comprising: (a) providing a linear system of fluid flow equations that represents fluid flow properties in a geological formation of a subterranean reservoir, the linear system of fluid flow equations comprising a plurality of unknown variables; (b) applying, with a processor, block diagonal scaling to the linear system of fluid flow equations to obtain a block diagonal matrix; (c) applying at least one of Sinkhorn-Knopp Column-Row equilibration, Sinkhorn-Knopp Row-Column equilibration, or Ruiz Row-Column equilibration; (d) applying threshold incomplete lower-upper approximate factorization to the block diagonal matrix to obtain a preconditioning matrix; and (e) iteratively solving the linear system of fluid flow equations for the unknown variables using the preconditioning matrix.