Parallel CPR preconditioner for a multicomponent fluid flow filtration problem in a porous medium

The constrained pressure residual (CPR) preconditioning method is considered with regard to solution of systems with matrices appearing in discretization of PDE systems describing multicomponent fluid flow in porous media. New versions of algorithms are proposed. Numerical experiments using an actual parallel hydrodynamic simulator were performed for test and actual oil fields in Western Siberia, these experiments confirm the efficiency of the methods.