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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations
 SPE journal 19 (2014), Nr.4, S.726736 ISSN: 1086055X ISSN: 19300220 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer SCAI () 
Abstract
Fully implicit blackoil simulations result in huge, often veryillconditioned, linear systems of equations for different unknowns (e.g., pressure and saturations). It is wellknown that the underlying Jacobian matrices contain both hyperbolic and nearly elliptic subsystems (corresponding to saturations and pressure, respectively). Because a reservoir simulation is typically driven by the behavior of the pressure, constrainedpressureresidual (CPR)type twostage preconditioning methods to solve the coupled linear systems are a natural choice and still belong to the most popular approaches. After a suitable extraction and decoupling, the computationally most costly step in such twostage methods consists in solving the elliptic subsystems accurately enough. Algebraic multigrid (AMG) provides a technique to solve elliptic linear equations very efficiently. Hence, in recent years, corresponding CPRAMG approaches have been extensively used in practice. Unfortunately, if applied in a straightforward manner, CPRAMG does not always work as expected. In this paper, we discuss the reasons for the lack of robustness observed in practice, and present remedies. More precisely, we will propose a preconditioning strategy (based on a suitable combination of left and right preconditioning of the Jacobian matrix) that aims at a compromise between the solvability of the pressure subproblem by AMG and the needs of the outer CPR process. The robustness of this new preconditioning strategy will be demonstrated for several industrial test cases, some of which are very illconditioned. Furthermore, we will demonstrate that CPRAMG can be interpreted in a natural way as a special AMG process applied directly to the coupled Jacobian systems.