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On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Sep 2018, Volume 2018, p.1 - 22
Abstract
We explore and develop POD-based deflation methods to accelerate the solution of large-scale linear systems resulting from two-phase flow simulation.
The techniques here presented collect information from the system in a POD basis, which is later used in a deflation scheme.
The snapshots required to obtain the POD basis are captured in two ways: a moving window approach, where the most recently computed solutions are used, and a training phase approach, where a full pre-simulation is run. We test this methodology in highly heterogeneous porous media: a full SPE 10 model containing O(10^6) cells, and in an academic layered problem presenting a contrast in permeability layers up to 10^6. Among the experiments, we study cases including gravity and capillary pressure terms.
With the POD-based deflated procedure, we accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method, reducing the required number of iterations to around 10–30 %, i.e., we achieve speed-ups of factors three to ten.