Application of conjugate‐gradient‐like methods to a hyperbolic problem in porous‐media flow

Abstract

Abstract This paper presents the application of a preconditioned conjugate‐gradient‐like method to a non‐self‐adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non‐symmetric matrices arising at each iteration of the non‐linear time‐stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.