HR: 1340h
AN: H23G-1723    [Abstracts]
TI: Simulation of Porous Flow and Transport in Heterogeneous Media Using Fractal Interpolating Functions
AU: * Travis, B
EM: bjtravis@lanl.gov
AF: Los Alamos National Laboratory, Earth and Environmental Sciences EES-2/MS-F665, LANL, NM 87545, United States
AB: Analogous to linear interpolation functions, fractal interpolation functions can be defined for fractally heterogeneous, multi-scale media. A fractal interpolating function (fif) is a continuous function that passes through a set of data points, and has the additional property that it is the attractor of an iterated function set (ifs). Each member of the ifs maps the entire domain into a subdomain, with the union of the subdomains covering the entire domain. Fractal (power law) behavior is a reasonable approximation to permeability scale dependence, at least over a range of scales. For media whose smaller-scale heterogeneity can be approximated by a fractal model, fifs provide a way to capture sub-gridscale properties and fluxes within a coarser finite difference or finite element grid. Advantages of this approach are that it can be incorporated into conventional finite difference or finite element codes, 2-D and 3-D applications are straightforward, and the solution can be recovered to any resolution desired. Several 2-D and 3-D examples illustrate the usefulness of this approach for transport in heterogeneous media.
DE: 0545 Modeling (4255)
DE: 1832 Groundwater transport
DE: 1839 Hydrologic scaling
DE: 1849 Numerical approximations and analysis
DE: 4440 Fractals and multifractals
SC: Hydrology [H]
MN: 2007 Fall Meeting