Decoupling and block preconditioning for sedimentary basin simulations

摘要

The simulation of sedimentary basins aims at reconstructing its historical evolution in order to provide quantitative predictions about phenomena leading to hydrocarbon accumulations. The kernel of this simulation is the numerical solution of a complex system of partial differential equations of mixed parabolic-hyperbolic type. A discretisation and linearisation of this system leads to large ill-conditioned nonsymmetric linear systems with three unknowns per mesh element. The preconditioning which we will present for these systems consists in three stages: (ⅰ) a local decoupling of the equations which (in addition) aims at concentrating the elliptic part of the system in the "pressure block"; (ⅱ) an efficient preconditioning of the pressure block using AMG; (ⅲ) the "recoupling" of the equations. In all our numerical tests on real case studies we observed a reduction of the CPU-time for the linear solver (up to a factor 4.3 with respect to the current preconditioner ILU(0)) and almost no degradation with respect to physical and numerical parameters.