Efficient Solution Techniques for Multi-phase Flow in Porous Media
Multi-phase flow in porous media is relevant for many applications, e.g. geothermal energy production, groundwater remediation, CO\(_2\) sequestration, enhanced oil recovery or nuclear waste storage. The arising non-linear partial differential equations are highly non-linear and thus often solved in a fully implicit way. We present a Schur complement reduction method relying on algebraic multigrid methods for solving the arising linear systems. This method is compared to a classical Constrained Pressure Residual (CPR-AMG) approach. It turns out that the new method is competitive to the classical approach with the advantage that it relies only on scalable algebraic multigrid (AMG) and not on incomplete LU (ILU) preconditioning. Scaling results are presented for both methods on the Jülich high performance computer JUQUEEN.
KeywordsMulti-phase flow Fully implicit newton method Constrained pressure residual (CPR-AMG) Algebraic multigrid (AMG) Schur complement reduction High performance computing (HPC)
The research leading to these results has received funding from the European Union’s Horizon2020 Research and Innovation Program under grant agreement No. 640573 (Project DESCRAMBLE) and No. 676629 (Project EoCoE).
We gratefully acknowledge the very helpful discussions with the PETSc developer team.
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