For the simulation of flow processes in the subsurface, complexity arises from various sources and reasons: First, geometry related aspects, such as anisotropies and heterogeneities of the porous medium, fractures and thin layers, or moving phreatic surfaces must be considered. Second, the underlying PDE is typically given as a transient problem with non-linear interactions and couplings between the physical unknowns.
Developing efficient solvers for these problems is not trivial, as suitable methods for spatio-temporal discretization and linear solvers must be com-bined into a scheme which is suitable for HPC architectures. In this study, we provide an overview and present a unified solver framework, which com-bines scalable multigrid solvers with a linearly-implicit extrapolation scheme.
The effectiveness of the approach is demonstrated for different appli-cations. These include (i) linear poroelasticity, which considers deforma-tions of the soil, (ii) density-driven flow in domains with a free groundwater surface, (iii) thermo-hydraulic flow, which features thawing and freezing in permafrost regions, and (iv) thermohaline flow, in which density depends on temperature and salt concentration. We investigate robustness of the numerical methods, develop suitable error estimators and provide scaling results in an HPC environment.
Arne Nägel is an academic researcher from Goethe University Frankfurt. He has contributed to research in topic(s): Multigrid method & Solver. He has an hindex of 8, co-authored 24 publication(s) receiving 200 citation(s).