David Benson

Professor, Geology and Geological Engineering

David Benson


Berthoud Hall 305C



  • Ph.D., Hydrogeology, University of Nevada, Reno, 1998
  • M.Sc., Geologic Sciences, San Diego State University, 1992
  • B.S., Geology, New Mexico State University, 1985

Research Areas

  • Fractional Calculus and Hydrology.
  • Mixing-Limited Chemical Reactions in Porous Media.
  • Numerical Methods, including Lagrangian Schemes.
  • Self-Similar Random Fields.


  • Benson, D. A., Pankavich, S., Schmidt, M. J., and Sole-Mari, G. (2020), Entropy: (1) The former trouble with particle-tracking simulation, and (2) A measure of computational information penalty, Advances in Water Resources 137, 103509, https://doi.org/10.1016/j.advwatres.2020.103509.
  • Benson, D. A, Schmidt, M. J., Bolster, D., Harmon, C., and Engdahl, N. (2019), Aging and mixing as pseudo-chemical-reactions between, and on, particles: Perspectives on particle interaction and multi-modal ages in hillslopes and streams, Advances in Water Resources 132 (2019) 103386, https://doi.org/10.1016/j.advwatres.2019.103386.
  • Sole-Mari, G., M. J. Schmidt, S. Pankavich, and D. A. Benson (2019), Numerical equivalence between SPH and probabilistic mass transfer methods for Lagrangian simulation of dispersion, Advances in Water Resources 126, 108-115, https://doi.org/10.1016/j.advwatres.2019.02.009.
  • Engdahl, N. B., M. J. Schmidt, and Benson, D. A. (2019), Accelerating and parallelizing Lagrangian simulations of mixing-limited reactive transport, Water Resources Research 55, https://doi.org/10.1029/2018WR024361.
  • Schmidt, M. J., Pankavich, S. D., Navarre-Sitchler, A., and Benson, D. A. (2019), A Lagrangian method for reactive transport with solid/aqueous chemical phase interaction, Journal of Computational Physics X (2), 100021, https://doi.org/10.1016/j.jcpx.2019.100021.
  • Benson, D. A., Pankavich, S, and Bolster, D. (2018), On the separate treatment of mixing and spreading by the reactive-particle-tracking algorithm: An example of accurate upscaling of reactive Poiseuille flow, Advances in Water Resources (123)doi:10.1016/j.advwatres.2018.11.001.
  • Schmidt, M. J., Pankavich, S. D., and Benson, D. A. (2018), On the accuracy of simulating mixing by random-walk particle-based mass-transfer algorithms, Advances in Water Resources (117) doi:10.1016/j.advwatres.2018.05.003.
  • Schmidt, M. J., Pankavich, S., and Benson, D. A. (2017), A kernel-based Lagrangian method for imperfectly-mixed chemical reactions, J. Computational Physics 336, 288–307, doi:10.1016/j.jcp.2017.02.012.
  • Ding, D., Benson, D. A., Fernandez-Garcia, D., Henri, C. V., Hyndman, D. W., Phanikumar, M. S., and Bolster, D. (2017), Elimination of the reaction rate “scale effect”: Application of the Lagrangian reactive particle-tracking method to simulate mixing-limited, field-scale biodegradation at the Schoolcraft (MI, USA) site, Water Resources Researchdoi:10.1002/2017WR021103.
  • Benson, D. A., Aquino, T., Bolster, D., Engdahl, N., Henri, C. V., and Fernandez-Garcia, D. (2017), A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms. Advances in Water Resources 99, 15 – 37, doi:10.1016/j.advwatres.2016.11.003.
  • Engdahl, N. B., Benson, D. A., and Bolster, D. (2017), Lagrangian simulation of mixing and reactions in complex geochemical systems, Water Resources Research 53, 4, 3513–3522, doi:10.1002/2017WR020362.
  • Bolster, D., Benson, D. A., and Singha, K. (2017), Upscaling chemical reactions in multicontinuum systems: When might time fractional equations work?, Chaos, Solitons & Fractals 102, Supplement C, 414 – 425. Future Directions in Fractional Calculus Research and Applications, doi:10.1016/j.chaos.2017.04.028.
  • Benson, D. A., and Bolster, D. (2016), Arbitrarily complex chemical reactions on particles, Water Resources Research 52, 11, 9190–9200, doi:10.1002/2016WR019368.
  • Bolster, D., Paster, A., and Benson, D. A. (2016), A particle number conserving Lagrangian method for mixing-driven reactive transport, Water Resources Research 52, 2, 1518–1527. doi:10.1002/2015WR018310.
  • Ding, D. and D. A. Benson (2015), Simulating biodegradation under mixing-limited conditions using Michaelis–Menten (Monod) kinetic expressions in a particle tracking model. Advances in Water Resources 76, 109 – 119, doi:10.1016/j.advwatres.2014.12.007.
  • Engdahl, N., D. A. Benson, and D. Bolster (2014), Predicting the enhancement of mixing-driven reactions in non-uniform flows using measures of flow topology, Physical Review E 90(5), 051001, doi:10.1103/PhysRevE.90.051001.
  • Dogan, M., R. L. Van Dam, G. Liu, M. M. Meerschaert, J. J. Butler, Jr., G. C. Bohling, D. A. Benson, and D. W. Hyndman (2014), Predicting flow and transport in highly heterogeneous alluvial aquifers, Geophysical Research Lettersdoi:10.1002/2014GL061800.
  • Pedretti, D., D. Fernandez-Garcia, X. Sanchez-Vila, D. Bolster, and D. A. Benson (2014), Apparent directional mass-transfer capacity coefficients in three-dimensional anisotropic heterogeneous aquifers under radial convergent transport, Water Resour. Res., doi:10.1002/2013WR014578.
  • Paster, A., D. Bolster, and D. A. Benson (2014), Connecting the dots: A comparison of semi-analytical and random walk numerical solutions of the diffusion-reaction equation with stochastic initial conditions, Journal of Computational Physics doi:10.1016/j.jcp.2014.01.020.
  • Benson, D.A., Bolster, D., & Paster A., 2013, The full subordination solution of the annihilation reaction A+B –> 0. J. Chemical Physics, 138, in press.
  • Meerschaert, M. M., Dogan, M., Van Dam, R.L., Hyndman, D.W., & Benson, D.A., 2013, Hydraulic conductivity fields: Gaussian or not? Water Resources Reserch, 49, in press.
  • Ding, D., Benson, D.A., Paster, A., & Bolster, D., 2013, Modeling bimolecular reactions and transport in porous media via particle tracking. Advances in Water Resources, 53, in press.
  • Bolster, D., Benson, D.A., Meerschaert, M.M., & Baeumer, B., 2013, Mixing-driven equilibrium reactions in multidimensional fractional advection dispersion systems. Physica A, 392, 2513-2525.
  • Paster, A., Bolster, D., & Benson, D.A., 2013, Particle tracking and the diffusion-reaction equation. Water Resources Research, 49, in press.
  • Benson, D. A., Meerschaert, M.M., & Revielle, J., 2013, Fractional calculus in hydrologic modeling: A numerical perspective. Advances in Water Resources, 51, 479-497.
  • Bolster, D., de Anna, P., Benson, D.A., & Tartakovsky, A.M., 2012, Incomplete mixing and reactions with fractional dispersion. Advances in Water Resources, 37, 86-93.
  • Major, E., Benson, D.A., Revielle, J., Ibrahim, H., Dean, A.M., Maxwell, R.M., Poeter, E.P., & Dogan, M., 2011, Comparison of Fickian and temporally non-local transport theories over many scales in an exhaustively sampled sandstone slab. Water Resources Research, 47, W10519.

Classes Taught

  • GEGN 581: Analytical Hydrology
  • GEGN 470: Groundwater Engineering Design
  • GEGN 583: Mathematical Modeling of Groundwater Systems
  • GEGN 598: Advanced Contaminant Transport