On The Acceleration Of Ill-Conditioned Linear Systems
A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow
Gabriela Diaz Cortes (TU Delft - Numerical Analysis)
J.D. Jansen (TU Delft - Geoscience and Engineering, TU Delft - Civil Engineering & Geosciences)
Kees Vuik (TU Delft - Numerical Analysis)
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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.