Preconditioner methods applied to simulations of two-phase flow in porous media

Simulations of two-phase flow in porous media require solving a set of linear equations which can be both large and sparse, and doing so repeatedly, to obtain local pressures under conditions of viscous flow. A variation of the incomplete cholesky preconditioned conjugate gradient solver has recently been developed for this purpose, and is presented here. It is found to be both stable and efficient. The variation consists of determining the sparsity structure of the preconditioner from a neighborhood search. Also, if the viscosities of the two fluids are different, the preconditioner should be updated during the course of the simulation. How often this should be done depends on the magnitude of the viscosity ratio, on the cost of updating the preconditioner and on how quickly the simulation configuration changes. To address this, a dynamic preconditioner update criterion is formulated.