Abstract
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.
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References
K. Aziz and A. Settari, Petroleum Reservoir Simulation (Elsevier, London, 1979).
S. Balay, W. Gropp, L. Curfman McInnes and B. Smith, PETSc users manual, Report ANL-95/11 (Revision 2.1.0), Argonne National Laboratory, IL (2001).
A. Behie and P.K.W. Vinsome, Block iterative methods for fully implicit reservoir simulation, Soc. Petroleum Engrg. J. 22 (1982), 658-668.
C.N. Dawson, H. Klie, M.F. Wheeler and C.S. Woodward, A parallel, implicit, cell-centered method for two-phase flow with a preconditioned Newton-Krylov solver, J. Comput. Geosci. 1 (1997) 215-249.
H.C. Edwards, A parallel multilevel-preconditioned GMRES solver for multi-phase flow models in the Implicit Parallel Accurate Reservoir Simulator (IPARS), TICAM Report 98-04, University of Texas, Austin (1998).
G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles non Linéaires de l'Ingénierie Pétrolière (Springer, Berlin, 1996).
S. Lacroix, Y.V. Vassilevski, J. Wheeler and M.F. Wheeler, Iterative solution methods for modeling multiphase flow in porous media fully implicitly, SIAM J. Sci. Comput. (2003) to appear.
S. Lacroix, Y.V. Vassilevski and M.F. Wheeler, Decoupling preconditioners in the implicit parallel accurate reservoir simulator (IPARS), Numer. Linear Algebra Appl. 8 (2001) 537-549.
Manuel utilisateur des calculateurs ViscoM1D et Visco3D, Technical Report, Institut Français du Pétrole, Rueil-Malmaison (2002).
R. Masson, P. Quandalle, S. Requena and R. Scheichl, Parallel preconditioning for sedimentary basin simulations, in: Proc. of the 4th Internat. Conf. on Large Scale Scientific Computations, 4–8 June 2003, Sozopol, Bulgaria, Lecture Notes in Computer Science, to appear.
J.W. Ruge and K. Stüben, Algebraic multigrid (AMG), in: Multigrid Methods, ed. S.F. McCormick, Frontiers in Applied Mathematics, Vol. 5 (SIAM, Philadelphia, 1986).
Y. Saad, Iterative Methods for Sparse Linear Systems (PWS Publishing, Boston, 1996).
F. Schneider, S. Wolf, I. Faille and D. Pot, A 3D basin model for hydrocarbon potential evaluation: Application to Congo Offshore, Oil and Gas Science and Technology–Rev. IFP 55 (2000) 3-13.
K. Stüben, Algebraic multigrid (AMG): Experiences and comparisons, Appl. Math. Comput. 13 (1983) 419-452.
H.A. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Comput. 12 (1992) 631-644.
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Scheichl, R., Masson, R. & Wendebourg, J. Decoupling and Block Preconditioning for Sedimentary Basin Simulations. Computational Geosciences 7, 295–318 (2003). https://doi.org/10.1023/B:COMG.0000005244.61636.4e
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DOI: https://doi.org/10.1023/B:COMG.0000005244.61636.4e