HR: 14:25h
AN: H12G-04    [PDF]
TI: A Novel Approach to Modeling of Hydrogeologic Systems Using Fuzzy Differential Equations
AU: * Faybishenko, B A
EM: bfayb@lbl.gov
AF: Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 90-1116, Berkeley, CA 94720 United States
AB: The many simultaneously occurring processes in unsaturated-saturated heterogeneous soils and fractured rocks can cause field observations to become imprecise and incomplete. Consequently, the results of predictions using deterministic and stochastic mathematical models are often uncertain, vague or "fuzzy." One of the alternative approaches to modeling hydrogeologic systems is the application of a fuzzy-systems approach, which is already widely used in such fields as engineering, physics, chemistry, and biology. After presenting a hydrogeologic system as a fuzzy system, the author presents a fuzzy form of Darcy's equation. Based on this equation, second-order fuzzy partial differential equations of the elliptic type (analogous to the Laplace equation) and the parabolic type (analogous to the Richards equation) are derived. These equations are then approximated as fuzzy-difference equations and solved using the basic principles of fuzzy arithmetic. The solutions for the fuzzy-difference equations take the form of fuzzy membership functions for each observation point (node). The author gives examples of the solutions of these equations for flow in unsaturated and saturated media and then compares them with those obtained using deterministic and stochastic methods.
DE: 1829 Groundwater hydrology
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2003 Fall Meeting