HR: 1340h
AN: H33F-0518    [Abstracts]
TI: Coupled versus Decoupled Solution Approaches for Non-Linear Fluid Flow Processes in Heterogeneous Porous and Fractured Media
AU: Burri, A
EM: burriad@student.ethz.ch
AF: ETH Zurich, Department of Mathematics Computational Science and Engineering Raemistrasse 101 , Zurich, 8092 Switzerland
AU: * Geiger, S
EM: geiger@erdw.ethz.ch
AF: ETH Zurich, Department of Earth Sciences Institute for Isotope Geology and Mineral Resources Sonneggstrasse 5, Zurich, 8092 Switzerland
AU: Coumou, D
EM: coumou@erdw.ethz.ch
AF: ETH Zurich, Department of Earth Sciences Institute for Isotope Geology and Mineral Resources Sonneggstrasse 5, Zurich, 8092 Switzerland
AB: Many fluid-flow processes in the Earth's crust, such as multiphase flow or convection due to temperature and/or concentration gradients, are non-linear in nature. Studying these processes using numerical simulations is challenging. On one hand, numerical methods must be robust and able to deal with the non-linearities efficiently. On the other hand, they must be capable of resolving orders of magnitude variations in permeability and geologically complex structures that often occur in the Earth's subsurface. This usually requires high-resolution meshes, possibly with up to several million degrees of freedom. Traditionally numerical methods have solved such flow processes fully coupled, i.e. solving for the independent variables simultaneously using iterative techniques to account for the non-linearities. While these approaches have solved challenging problems, they have the disadvantage that the global solution matrices are ill conditioned and hence not always suitable for fast matrix solvers such as algebraic multigrid solvers. Furthermore, iterative techniques such as Newton's method may fail to converge. Numerical approaches that are capable of resolving geologically complex structures, for example the finite element method, require upwind-weighting schemes to model advection-dominated fluid flow. Such upwinding techniques, however, may reduce the geometric flexibility of the finite element method, fail to converge if the permeability varies over more than two orders of magnitude, or smear out shock fronts in advection-dominated flows. Here we present the solutions of a decoupled approach, based on a combination of finite volume and finite element methods, and a fully coupled approach, based on an upwind-weighted finite element method, for a variety of non-linear fluid flow problems. The results are compared for accuracy, robustness, and speed. They show that, in general, the decoupled approach is computationally more efficient and robust, because it does not require the use of costly iteration schemes. The decoupled approach can particularly well deal with orders of magnitude variations in permeability. Since higher-order finite volume methods are used in the decoupled approach to solve the advection equations, shock fronts in advection-dominated processes are retained to great accuracy. The exactness of the solutions of the decoupled approach can be improved even further by using internal Picard iterations or improved Euler time-stepping. Results for simulations of convection in sub-seafloor magmatic-hydrothermal systems, where temperature variations are in excess of 1000$^\circ$C, however, show that the gain in accuracy is only small and does not justify the increased computational costs.
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3230 Numerical solutions
DE: 1829 Groundwater hydrology
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting