Professor Myron Allen

Myron Allen, Ph.D., Princeton University Professor of Mathematics Ross Hall 228 allen@uwyo.edu | +1-307-766-4221 Research interests: Numerical analysis and Mathematical modeling

Education

Ph.D., Princeton University, 1983
M.A., Princeton University, 1978
A.B., Dartmouth College, 1976

About Dr. Allen

Myron Allen joined the University of Wyoming faculty in 1983. He came to the University of Wyoming from Princeton University.

His mathematical interests include numerical analysis, mathematical modeling, and fluid mechanics in porous media. Applications of these areas include the analysis and prediction of contaminant flows in groundwater aquifers and flows of native and injected fluids in oil and gas reservoirs.

Flows of this type obey a remarkable variety of partial differential equations, including equations of elliptic, parabolic, and hyperbolic type as well as nonlinear, coupled systems having mixed type. The equations generally require numerical solution. Numerical methods of interest include mixed finite elements, cell-centered finite-differences, Eulerian-Lagrangian methods such as the modified method of characteristics, streamline diffusion methods, and finite-volume methods.

To model porous-media flows found in nature, one must address some physical issues that cause severe numerical difficulties. First, the equations are often nonlinear, so one must devise sensitive iterative schemes based, for example, on Newton's method. Second, the equations often have solutions with steep gradients, near which most numerical methods yield poor approximate solutions. Third, the equations sometimes include chemical or biological reactions, which involve complicated thermodynamic constraints or reaction-diffusion structures, such as traveling waves. Fourth, to accommodate natural geologic heterogeneity, one must account for differences in scale between the measurements used to determine model inputs and the computational grids used to solve the problems.

Representative Publications

1. M.B. Allen and E.L. Isaacson, Numerical Analysis for Applied Science, 2^ndedition, John Wiley & Sons, Hoboken, NJ, 2018 (568 pages).
2. Ogden, M.B. Allen, W. Lai, J. Zhu, M. Seo, C.C. Douglas, C. Talbot, “The soil moisture velocity equation,” Journal of Advances in Modeling Earth Systems9 (2017), https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017MS000931.
3. S. Telyakovskiy, S. Kurita, and M.B. Allen, “Polynomial-based approximate solutions to the Boussinesq equation near a well,” Advances in Water Resources96 (2016), 68-73, https://www.sciencedirect.com/science/article/pii/S0309170816301932.
4. M. B. Allen, Continuum Mechanics: The Birthplace of Mathematical Models, John Wiley & Sons, Hoboken, NJ, 2015 (304 pages).