Random porous media flow on large 3-D grids: Numerics, performance, and application to homogenization
- Commissariat a l`Energie Atomique Saclay, Gif-sur-Yvette (France)
Subsurface flow processes are inherently three-dimensional and heterogeneous over many scales. Taking this into account, for instance assuming random heterogeneity in 3-D space, puts heavy constraints on numerical models. An efficient numerical code has been developed for solving the porous media flow equations, appropriately generalized to account for 3-D, random-like heterogeneity. The code is based on implicit finite differences (or finite volumes), and uses specialized versions of pre-conditioned iterative solvers that take advantage of sparseness. With Diagonally Scaled Conjugate Gradients, in particular, large systems on the order of several million equations, with randomly variable coefficients, have been solved efficiently on Cray-2 and Cray-Y/MP8 machines, in serial mode as well as parallel mode (autotasking). The present work addresses, first, the numerical aspects and computational issues associated with detailed 3-D flow simulations, and secondly, presents a specific application related to the conductivity homogenization problem (identifying a macroscale conduction law, and an equivalent or effective conductivity). Analytical expressions of effective conductivities are compared with empirical values obtained from several large scale simulations conducted for single realizations of random porous media.
- OSTI ID:
- 505168
- Report Number(s):
- CONF-9207256-Vol.79; TRN: 97:003314-0001
- Resource Relation:
- Conference: IMA summer program on mathematical, computational, and statistical analyses in environmental studies, Minneapolis, MN (United States), 6-31 Jul 1992; Other Information: PBD: 1996; Related Information: Is Part Of Environmental studies: Mathematical, computational, and statistical analysis; Wheeler, M.F. [ed.] [Rice Univ., Houston, TX (United States)]; PB: 414 p.
- Country of Publication:
- United States
- Language:
- English
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