School of Mathematical Sciences

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Donald Brown

Assistant Professor of Applied Mathematics, Faculty of Science



I am an Assistant Professor of Applied Mathematics in the School of Mathematical Sciences, having started in September 2015. I am also associated with the GeoEnergy Research Center (GERC), a joint venture between the British Geological Society (BGS) and the University of Nottingham. I work with the Scientific Computing group, but also have close overlap in areas of industrial and applied mathematics. Broadly speaking, I work in the area of modeling and numerical analysis on problems arising in porous media with an emphasis in geosciences.

Before arriving in Nottingham, I completed my PhD in Applied Mathematics at Texas A&M University, USA in 2012 and went as a postdoctoral research fellow at the Center for Numerical Porous Media, King Abdullah University of Science and Technology, Saudi Arabia from 2012-2014. Then, I was awarded the Hausdorff Postdoctoral Fellowship, at the University of Bonn, Germany, and from 2014-2015 worked in the Institute for Numerical Simulation in Bonn.

GeoEnergy Research Center



Expertise Summary

My research focus is on multiscale modeling and simulation of subsurface porous media and developing applicable mathematical tools and techniques. The research has wide ranging applications in the modeling of subsurface flows for oil and gas and hydrological applications. Many porous media processes have significant multiscale and multi-physical characteristics. This multiscale nature of porous media often makes solving the full problem intractable and alternative techniques must be employed to bridge these scales. My research is to develop computational tools and analysis techniques to deal with fundamental problems in multiscale processes of subsurface physics. I am interested in homogenization theory of partial differential equations to obtain effective physical models, multilevel upscaling with complex physics and uncertainty, and development and analysis of multiscale methods for subsurface reservoirs. My research has also focussed on the application of model reduction techniques to lattice Boltzmann methods for pore-scale simulations using the Brinkman flow models, phase field modeling, and multiscale finite elements with porous microstructures. Recently, I have worked on multiscale localization for heterogeneous Helmholtz equations for acoustic and seismic applications.

Teaching Summary

Current Teaching:

HG2M02: Applied Algebra. Spring Semester 2015-16

HG1MMC: Civil Engineering Mathematics. Spring Semester 2016-17

Research Summary

Computational tools and techniques:

Multiscale modeling and simulation of porous media.

Geomechanics and fluid-solid geochemical interaction in subsurface media.

Developing multiscale finite element, local orthogonal decomposition, and multilevel upscaling methods.

Effective equations for fundamental porous media and materials models.

Lattice Boltzmann methods for pore-scale simulations.

Phase field modeling of interfaces.

Application Areas:

Conventional Energy : Shale gas, coal bed methane, enhanced oil recovery, carbonate reservoirs.

Renewable Energy: Geothermal, Enhanced Geothermal Systems.

Environmental Ares: Groundwater flow, surface subsidence and compaction, earth observation, integration of data into subsurface models.

Cross-Cutting: Porous media models for filtration devices and lithium-Ion batteries.

Recent Publications

Currently Funded Postgraduate Phd Projects:

Please look at the GERC website for current vacancies.

Possible Postgraduate Phd Projects

Self-funded Phd (or Postdocs) students with interests and expertise in numerical analysis, subsurface modeling or more broadly porous media theory are welcome.

Postdoctoral opportunities

Other opportunities

The Newton Fund has many interesting opportunities at various career levels for researchers based in:

"Brazil, Chile, China, Colombia, Egypt, India, Indonesia, Kazakhstan, Malaysia, Mexico, Philippines, South Africa, Thailand, Turkey, Vietnam",

to collaborate and visit with UK based researchers. These include bi-lateral visits, workshops and industry engagement, Phd student travel and exchanges, postdoctoral research fellowships, and even Newton Advanced Fellowships for advanced career researchers.

Inquiries related to this program in the areas of GeoEnergy, environmental, and in general subsurface modeling are also welcome.

  • P. VIGNAL, N. COLLIER, L. DALCIN, D.L. BROWN and V. CALO, 2017. An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering. 316, 1179–1214
  • COLLIS, J, BROWN, DL, HUBBARD, ME and O'DEA, RD, 2017. Effective Equations Governing an Active Poroelastic Medium Proceedings of the Royal Society A. 473, 20160755
  • D. L. BROWN and V. H. HOANG, 2017. A Hierarchical Finite Element Monte Carlo Method for Stochastic Two-Scale Elliptic Equations Journal of Computational and Applied Mathematics. 323, 16-35
  • D.L. BROWN, D. GALLISTL and D. PETERSEIM, 2017. Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations. In: GRIEBEL M. and SCHWEITZER M., eds., Meshfree Methods for Partial Differential Equations VIII 115. Springer, Cham. 85-115
  • D.L. BROWN and MARIA VASILYEVA, 2016. Generalized Multiscale Finite Element Method for Poroelasticity Equations I: Linear Problems Journal of Computational and Applied Mathematics. 294(C), 372-388
  • D.L. BROWN and M. VASILYEVA, 2016. Generalized Multiscale Finite Element Method for Poroelasticity Equations II: Nonlinear Coupling Journal of Computational and Applied Mathematics. 297, 132-146
  • V. TARALOVA and D.L. BROWN, 2016. A multiscale finite element method for Neumann problems in porous microstructures Disc. and Cont. Dyn. Sys Series S. 9(5), 1299-1326.
  • D.L. BROWN and D. PETERSEIM, 2016. A Multiscale Method for Porous Microstructures SIAM, Multiscale Modeling and Simulation. 14(3), 1123–1152.
  • P. VIGNAL, N. COLLIER, L. DALCIN, D.L. BROWN and V. CALO, 2015. An Energy-Stable Convex Splitting for the Phase-Field Crystal Equation Computers & Structures. 158, 355–368
  • D.L. BROWN, G. LI, V.L. SAVATOROVA and Y. EFENDIEV, 2014. Homogenization of Brinkmann equations with High-Contrast Coefficients SIAM Multiscale Modeling and Simulation. 13(2), 472–490
  • D.L. BROWN, V. H. HOANG and Y. EFENDIEV, 2013. An Efficient Hierarchical Multiscale Finite Element Method for Stokes Equations in Slowly Varying Media SIAM Multiscale Modeling and Simulation. 11(1), 30-58
  • D.L. BROWN, P. POPOV and Y. EFENDIEV, 2013. Effective Equations for Fluid-Structure Interaction with Applications to Poroelasticity Applicable Analysis. 93(4), 771-790
  • D. L. BROWN., P. POPOV and Y. EFENDIEV, 2011. On homogenization of stokes flow in slowly varying media with applications to fluid–structure interaction Int. J. of Geomathematics. 2(2), 281-305

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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