A domain decomposition algorithm using triangular subdomains has been developed to solve steady flow problems in randomly heterogeneous porous media. In each triangle three adjoint solutions are sought by traditional finite elements. These solutions, which incorporate the actual non-homogeneities of the permeability field and may be evaluated simultaneously on a parallel machine, provide adjoint fluxes to be subsequently integrated over the subdomain boundaries and properly assembled over the nodes of the macromesh. A final algebraic unsymmetric system is thus arrived at, whose solution gives the head on the nodes of the subregions or macromesh. The formulation fully includes the effects of the heterogeneity distribution at the microscale. The approach appears to be particularly suited to randomly heterogeneous media.
Domain Decomposition for Randomly Heterogeneous Porous Media
SARTORETTO, Flavio
1990-01-01
Abstract
A domain decomposition algorithm using triangular subdomains has been developed to solve steady flow problems in randomly heterogeneous porous media. In each triangle three adjoint solutions are sought by traditional finite elements. These solutions, which incorporate the actual non-homogeneities of the permeability field and may be evaluated simultaneously on a parallel machine, provide adjoint fluxes to be subsequently integrated over the subdomain boundaries and properly assembled over the nodes of the macromesh. A final algebraic unsymmetric system is thus arrived at, whose solution gives the head on the nodes of the subregions or macromesh. The formulation fully includes the effects of the heterogeneity distribution at the microscale. The approach appears to be particularly suited to randomly heterogeneous media.
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