On the convergence of system-AMG in reservoir simulation

System-AMG provides a flexible framework for linear systems in simulation applications that involve various different types of physical unknowns. Reservoir simulation applications, with their driving elliptic pressure unknown, are principally well-suited to exploit System-AMG as a robust and efficient solver method. However, in order to be efficient and robust, the coarse grid correction process of AMG on the one hand needs to be possible, i.e., the matrix needs to fulfill certain requirements. It has been demonstrated earlier how to ensure this by the dynamic rowsumming (DRS) method. On the other hand, the coarse grid correction must be physically meaningful in order to speed up the overall convergence. It has been common practice in CPR-type applications to use an approximate pressure-saturation decoupling to fulfill this requirement. This, however, can have drastic impacts on AMG's applicability and, thus, is not performed by the DRS-method. In this work, we are going to see that the pressure-saturation decoupling indeed is not necessary for ensuring an efficient interplay between the coarse grid correction process and the fine-level problem. We will find that a comparable influence of the pressure on the different involved PDEs is much more crucial. As an extreme case w.r.t. the outlined requirement, we will discuss linear systems from compositional simulations under the volume balance formulation. In these systems, the pressure typically is associated with a volume-balance, rather than a diffusion process. The corresponding coarse grid correction does, hence, not provide any benefit regarding the overall convergence: the other PDEs involve pressure-based diffusive parts that have a drastically different structure than the volume-balance has. We will see how System-AMG can still be used in such cases.