Modeling ground-water flow by means of a hybrid trajectory image, boundary integral equation method
Abstract
The trajectory image method (TIM), a new modeling technique based on image theory, can be used to find head, gradients, velocities, and flow directions. TIM derives from the idea that particles emitted by sources or adsorbed by sinks may be reflected by impermeable boundaries, or they may be partially absorbed, reflected, and partially transmitted by boundaries of differing hydraulic conductivities but with abrupt changes in their hydraulic heads. Particles move until their changes in head become negligible. Each reflection represents an image in terms of the boundaries where the trajectories are reflected, thus a great number of imaginary points, depending on accuracy desired after projection, are generated. The traveling distances of particles are measured from sources or sinks to the current ray-boundary intersections. Then the total head and gradients at each observation point are found by superposing heads and gradients of particle trajectories that pass through or close to the observation point. The number of reflections for each trajectory depends on the geometry of the boundary. TIM offers the following advantages for modeling ground-water flow with point or line sources and sinks: (1) Unlike finite difference and finite element methods, TIM does not magnify errors near sources or sinks; (2) Unlike the boundary integral equation method (BIEM), near-boundary computations are very accurate, and complicated integrations are avoided under unsteady-state condition; (3) Only zones with differing hydraulic conductivities have to be discretized; (4) Ease in modeling flow through anisotropic media without requiring that principal directions be parallel to coordinate directions or be transformed into other coordinate systems; and (5) Problem setup is much easier than in above methods. Although TIM requires considerably more computing time with standard mainframes, run times were reduced by an order of magnitude with a supercomputer. Also a combination of TIM and BIEM (TIMBIE) can reduce time requirements because of elimination of interpolation at internal accounting points. This testing procedure is rather reliable and convenient in comparing the values at all interior points, because both methods are completely independent of each other at accounting points (nodes). (Abstract shortened with permission of author.)
Degree
Ph.D.
Advisors
Leap, Purdue University.
Subject Area
Hydrology
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