HR: 14:20h
AN: H22G-03    [PDF]
TI: Approximate Similarity Solutions to the Boussinesq and the Porous Medium Equations.
AU: * Telyakovskiy, A S
EM: alekseyt@unr.edu
AF: Department of Mathematics, University of Nevada, Reno, NV 89557 United States
AB: The Boussinesq equation models unconfined groundwater flow under the Dupuit assumpion that the equipotential lines are vertical, making the flowlines horizontal. For certain classes of initial and boundary conditions it is possible to reduce problem to a nonlinear ODE and construct approximate analytical solutions. We extend the approach of Lockington, Parlange, Parlange, and Selker (2000) that constructed quadratic approximate similarity solution for the power-law head boundary condition at the inlet. Our new cubic approximation as the original quadratic approximation preserves the scaling properties of the problem, but it produces much better results. Also, we extend this approach to other types of boundary conditions. Discussed method is rather general and we apply it to the porous medium equation that describes the laminar flow of the polytropic gas through porous media.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1875 Unsaturated zone
SC: Hydrology [H]
MN: 2003 Fall Meeting