Universität zu Köln

Gries, Sebastian (2015). System-AMG Approaches for Industrial Fully and Adaptive Implicit Oil Reservoir Simulations. PhD thesis, Universität zu Köln.

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Abstract

A continuous increase of sub-surface flow models in size and physical complexity makes efficient and reliable linear solution approaches crucial for successfully applying reservoir simulations. Due to the essential objective of simulating diffusive fluid flux, algebraic multigrid methods are a natural option to consider. However, the application may not be straight-forward, as the solver has to cope with linear systems that are influenced by various physical effects. In this thesis we will discuss AMG-based solution approaches for Black-Oil and compositional models for fluid flow, as well as for models that additionally take thermal and mechanical effects into account. We will discuss the properties of the matrices that describe the linear systems and we will see the impact of different simulated effects. As Black-Oil models form the basis also for more sophisticated models, we will discuss a robust System-AMG approach for these simulations first. This will include preparatory matrix transformations that aim at ensuring the applicability of AMG. With this approach, we will be able to solve highly challenging problems from industrial simulations robustly and efficiently. We will then extent this approach to compositional, thermal and geomechanical problems. Finally, we will discuss some aspects of further improving the performance of System-AMG. This will involve algorithmic modifications that give AMG approaches with better computational efficiency, but we will also discuss some implementational aspects, e.g. regarding concurrency of incomplete factorizations.