### Leading Edge Numerical Modeling in Vadose Zone Ground Water Flow and Transport

This site was dedicated to the proposition that there are still advances to be made in the numerical modeling of below-surface unsaturated ground water flow. It demonstrates the research product of a disabled investigator between about October 1998 and February 2003, with the addition of a surface water dam breach study in 2002. It also contains soil physics and finite difference numerical modeling tutorials written while I was a Technical Assistant to Dr. H. Don Scott when he was at the University of Arkansas, Fayetteville.

Note: This is not the web site for Ballard's Frame Distributors. The robots that search the net for filler material in the various free directories aren't that smart.

A website chronology and new material can be found here

The soil physics and finite difference tutorials are consistently the most popular parts of the site. The soil physics tutorials range in difficulty from sophomore to the senior/graduate/postdoctoral level. They begin with the basics and extend to a new (2001) exact solution to Richards' equation for unsaturated horizontal and vertical flow, which reduces it to a numerical solution of an ordinary differential equation under given conditions. It solves both horizontal imbibition and vertical (top down) infiltration with either pressure or flow inflow boundary conditions. This particular solution solves in steps of saturation instead of space, making the wetting front very well defined regardless of sharpness or depth. New fine details and behaviors are visible that numerical models based on space and time cannot resolve.

The finite differences tutorial is a brief and limited tutorial in the use of finite difference methods to solve problems in soil physics. It is meant for students at the graduate and undergraduate level who have at least some understanding of ordinary and partial differential equations. After an explanation of how to use finite differences in cook-book fashion, the equations, computer code and graphic results are given for three examples: heat flow, infiltration and redistribution, and contaminant transport in a steady-state flow field.

The analysis of a set of dam breach physical models covered roughly three regimes: 1) breach flow without any head cut below the bottom, horizontal lip of the breach, 2) breach flow with a head cut below the lip of the breach, with a fully-aerated breach jet, and 3) breach flow into a head cut with the breach jet presumably without aeration (there were no measurements to confirm that, but significant deviations showed in the data at the highest flows). The conclusions for each case are: 1) breach flow without a head cut follows the NWS/Fread BREACH model of flow through a trapezoidal channel, 2) when an aerated jet falls into a head cut, a term related to the upstream head to the 5/2 power and the upstream slope of the dam is necessary, and the flow in that term can be several times the rest of the flow, and 3) losing aeration with increasing upstream head forces condition (2) back towards condition (1). There was not enough data to fully describe the nature and head-discharge function of condition (3). If conditions (2) or (3) exist in a breach with head cut, relying upon (1) to model the breach flow can vastly underestimate it. The 1889 Johnstown flood, www.nps.gov/jofl, for example, an earthen dam failed and killed 2209 people, about 2/3 the number of people killed in the 9/11 terrorist attack.

The gist of the research in Darcian intergrid unsaturated conductivity means for finite difference models of Richards' Equation is that the integral mean of unsaturated mean with matric suction is best for horizontal flow. For a homogeneous soil, it should be possible to create an interpolated integration table for the horizontal mean, integrating from infinite matric suction. The intergrid unsaturated mean for vertical flow is immensely complicated by gravity in combination with space step size, making its calculation daunting to say the least. Therefore, for vertical flow, where it is impractical to calculate the Darcian mean, it is this investigator's judgement that the simple upstream mean is second best.

The harmonic, geometric and arithmetic means and the like should be studiously avoided, as they can cause very non-physical behavior. I did not get to study conductivity means at interfaces between different soil layers. But I think that putting a mean across an interface is a bad idea. Just because a harmonic mean can be created that way from assumptions doesn't make it right. I submit that the difficulty might be solved by splitting a cell in two and puting the pressure grid point right on the interface.

This site has been as large as 60 Mb, including a section of the author's artwork. Because of illness, disability and the lack of research and educational support, this investigator has left the field in favor of developing artwork as a means to adding to disability income. If there is anyone who wishes to support parts of the site, or set up a mirror site, please contact me.

Legal notice: Although the information in this site was created in good faith, use it at your own risk.

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