Kris Kuhlman Sandia National Laboratories Repository Performance Department Carlsbad phone : (575) 234-0084 Albuquerque ph : (505) 845-0938 klkuhlm <at> sandia <dot> gov

I am an environmental engineer in the repository performance group at Sandia National Lab in Carlsbad, NM. I work on groundwater hydrology and modeling related to the WIPP, which is the only nuclear waste repository for TRU waste in the United States (see DOE website, and recent YouTube video for more about the WIPP). The WIPP is located in bedded salt – the Permian-age Salado formation; most of the hydrology work I am doing at WIPP is related to the overlying dolomites and evaporites.

I obtained my PhD in Hydrology under Shlomo P. Neuman (with a minor in mechanical engineering) at the University of Arizona in 2008. My dissertation was on the topic of transient analytic elements (LT-AEM); it is a semi-analytic method for solving the diffusion equation for separable geometries, utilizing the numerical inverse Laplace transform to allow general solutions to be computed in the time domain without resorting to contour integrations or time-domain convolution. I obtained my undergraduate degree in Geological Engineering (geotechnical engineering emphasis) from Colorado School of Mines in 1998.

Research interests

Coupled Hydrologic and Geophysical Problems

I have implemented the numerical solution of two coupled hydrologic / geophysical problems (1 2) for flow to a pumping well. In these problems, the observed electrical response is due to the electrokinetic effect (i.e., voltage arising due to an electrolyte being forced through pores or fractures). These coupled problems are interesting from both an analytic and numerical point of view.

Numerical inverse Laplace and Hankel transforms

My Fortran90 implementations of these numerical transform can be seen in my dissertation and papers with Malama (1 2 3 4) below. The Laplace transform allows time-dependent problems (e.g., the diffusion or wave equations) to be transformed into a type of steady-state problem (i.e., the modified Helmholtz equation, which is similar in form to the Hamiltonian operator from quantum mechanics) that only depends on a parameter, rather than an independent variable.

I have worked with various numerical schemes for inverting either Laplace or Hankel transforms, recently having settled on a fairly efficient and accurate numerical double inversion scheme (see Appendix B of Malama et al., 2009b and associated code below). I also performed a comparison between different numerical inverse Laplace transform approaches using a transient boundary element model as the test function

Special functions

I am working with special functions related to their use for solving PDEs. I have worked especially in elliptical coordinates, where modified Mathieu functions are useful for solving the modified Helmholtz equation (see my Python library, dissertation, and Kuhlman & Warrick below). I have a side interest in special functions that are solutions to inhomogeneous differential equations (e.g., Struve functions are solutions to the inhomogeneous Bessel equation).

Analytic elements

I am interested in AEM elements, specifically ones developed through separation of variables on the modified Helmholtz equation (see below LT-AEM code, Kuhlman & Neuman (2006), Kuhlman (2008), and Kuhlman & Neuman (2009)). The following are some curious animations I made for a introduction to hydrology class from steady-state AEM solutions for a circular region of different properties and a well.

1. a circular element in a uniform flow-field, where the permeability of the circle changes from very low to very high (compared to the background permeability).
2. a circular element with higher permeability than the background, but now the well moves around the circle.
3. a low-permeability circular element with a moving well, circle permeabilty is lower, but it is otherwise similar to the previous one.

Kriging and geostatistics

I am using kriging and various aspects of geostatistics which are useful in many different ways to hydrologists for both practical (kriging and cokriging; see Kuhlman & Pardo-Igúzquiza, 2010 below) and theoretical (stochastic hydrology) reasons, including tomography (see Kuhlman et al., 2008 below).

Unsaturated zone flow

I am interested in closed-form expressions for moisture retention curves, for use in numerical simulation of Richards equation (i.e., Hydrus). I am also interested in analytic solutions to various linearized forms of Richards equation (see Kuhlman & Warrick below).

Publications

• Kuhlman, K.L., and E. Pardo-Igúzquiza, 2010. Universal cokriging of hydraulic heads accounting for boundary conditions, Journal of Hydrology, 384(1–2), 14–25. (download draft copy and code)
• Malama, B., K.L. Kuhlman, and A. Revil, 2009. Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers, Geophysical Journal International, 179(2), 990–1003. (download code)
• Kuhlman, K.L. and S.P. Neuman, 2009. Laplace-transform analytic-element method for transient porous-media flow, Journal of Engineering Mathematics, 64(2), 113–130. (download draft copy and code)
• Malama, B., A. Revil, and K.L. Kuhlman, 2009. A semi-analytical solution for transient streaming potentials associated with confined aquifer pumping tests, Geophysical Journal International, 176(3), 1007–1016. (download code)
• Malama, B., K.L. Kuhlman, and W. Barrash, 2008. Semi-analytical solution for flow in a leaky unconfined aquifer toward a partially penetrating pumping well, Journal of Hydrology, 356(1-2), 234–244. (download draft copy and code)
• Kuhlman, K.L., 2008. Laplace transform analytic element method for transient groundwater flow simulation, PhD Dissertation, University of Arizona. (also available on Amazon, ISBN:9783639074314 and code)
• Kuhlman, K.L. and A.W. Warrick, 2008. Quasilinear infiltration from an elliptical cavity, Advances in Water Resources, 31(8), 1057–1065. (download draft copy and code)
• Kuhlman, K.L., A.C. Hinnell, P.K. Mishra, and T.-C.J. Yeh, 2008. Basin-scale transmissivity and storativity estimation using hydraulic tomography, Ground Water, 46(5), 706–715. (download draft copy)
• Malama, B., K.L. Kuhlman, and W. Barrash, 2007. Semi-analytical solution for flow in leaky unconfined aquifer-aquitard systems, Journal of Hydrology, 346(1-2), 59–68. (download draft copy and code)
• Kuhlman, K.L., and S.P. Neuman, 2006. Recent Advances in LT-AEM Theory and Application to Transient Groundwater Flow in Proceedings of the conference on Computational Methods in Water Resources XVI, Copenhagen, Denmark. (download code)

Email me (klkuhlm <at> sandia <dot> gov) if you would like a pdf copy of a published paper, but you do not have the proper institutional subscription (as per journal rules only draft copies and links to journal websites are given above).

Computer Codes

All codes are as-is; there is no warranty as to their accuracy. Any comments or problems can be sent to klkuhlm <at> sandia <dot> gov; I will try my best to help or accommodate you. Most of the codes are scripts or un-compiled source code with a Linux-style makefile. If you cannot compile or run the code yourself, I may be able to help you compile it or set up the right environment to get it working.

For most of the computer codes below, the files are available both as a zip archive for easy download (ZIP) and as a directory for browsing (DIR). The LT-AEM code is provided as a read-only link to my Mercurial repository (DCVS).

• (DCVS) · Laplace Transform Analaytic Element (LT-AEM) A Fortran-2003 program that implements the LT-AEM for circular (including wells as a special case) and elliptical elements (including lines as a special casae). This code is a work in progress, but it is functional and useful.
• (ZIP) (DIR) · Leaky-unconfined aquifer flow solution
  A Fortran90 program for computing the leaky-unconfined solutions discussed in Malama, Kuhlman & Barrash (2007 & 2008). This program does the double numerical inverse Laplace and Hankel transforms required to compute the time-domain solutions given in the papers. A Windows binary and fairly complete documentation is included.
• (ZIP) (DIR) · Electrokinetic pumping test response solution
  A Fortran90 program for computing the electrokinetic response due to pumping a well in an unconfined system, as discussed in (Malama et al., 2009b). The Stehfest algorithm is used for the numerical Laplace inverse transform, while a combination of tanh-sinh quadrature and accelerated Gauss-Lobatto quadrature (between the zeros of the J₀ Bessel function) is used for the numerical Hankel inverse transform. These algorithms are much faster and more accurate than the algorithms used in the leaky-unconfined papers listed above.
• (ZIP) (DIR) · Unsaturated flow from an elliptical pipe
  A set of MATLAB scripts for computing Quasilinear infiltration solutions from the paper above (Kuhlman & Warrick, 2008). These scripts compute the required ratios of Mathieu functions, compute the solution, and plot the figures shown in the paper.
• (ZIP) (DIR) · modified Mathieu functions of complex Mathieu parameter
  A Python module for computing both angular and radial modified Mathieu functions (and their derivatives with respect to argument) of integer order and general complex Mathieu parameter (Re(q)<0), see a pdf summary of Mathieu function library output, and a numerical comparison to a published C++ Mathieu function library for real q (Alhargan, 2000). My Python module requires numpy and scipy.
• (ZIP) (DIR) · Kriging hydraulic heads and boundary conditions
  A set of MATLAB scripts for cokriging heads taking boundary conditions into account from the paper above (Kuhlman & Pardo-Igúzquiza, 2010). These scripts set up and solve the cokriging equations using either the true derivative or finite-difference approximations described in the paper.
• (ZIP) (PDF) · Scrabble rhyming word lists
  A rhyming dictionary, where words are sorted alphabetically, starting at the last letter of the word, working back towards the front of the word. These are useful, for example, when you are trying to think of all the legal Scrabble words that that end in “–uppy” or “–ing”, etc. The Python code used to generate the lists from the standard Scrabble word lists, and the Python scripts used to create the LaTeX, that are then used to generate the pdf (e.g., see 11-letter word list), are included in the zip file.

Links