About

Jonathan J. L. Higdon is the Dennis and Cathy Houston Professor in Chemical and Biomolecular Engineering at the University of Illinois Urbana-Champaign. An award-winning teacher and scholar, he is a leader in the field of fluid mechanics. His research interests include computational fluid dynamics, the mechanics of complex fluids, geophysical fluid dynamics, and petroleum reservoir simulation. Dr. Higdon joined the department in 1980 and has contributed to investigating geophysical fluid dynamics associated with the evolution of meandering rivers, developing simulations for large-scale systems of hyperbolic partial differential equations for petroleum reservoirs and geophysical transport processes, and studying the micro-scale dynamics of complex fluids. He received his B.E.S. and M.S.E. from Johns Hopkins University and his Ph.D. in Applied Mathematics and Theoretical Physics from Cambridge University, where he was a Winston Churchill Scholar and a National Science Foundation Fellow. He completed his postdoctoral studies at Stanford University.

Research topics

• Mathematics
• Physics
• Mathematical analysis
• Geology
• Mechanics
• Applied mathematics
• Geotechnical engineering
• Geometry
• Geomorphology

Selected publications

• A fully-implicit hybridized discontinuous Galerkin spectral element method for two phase flow in petroleum reservoirs

  Journal of Computational Physics · 2022 · 3 citations

  Senior authorCorresponding
  • Mathematics
  • Applied mathematics
  • Mathematical analysis
  PublisherDOI

• Dynamics of meandering rivers in finite-length channels: linear theory

  Journal of Fluid Mechanics · 2022 · 10 citations

  Senior authorCorresponding
  • Mechanics
  • Geology
  • Geometry

  Meandering channels are dynamic landforms that arise as a result of fluid mechanic and sedimentary processes. Their evolution has been described by the meander-morphodynamic equations, which dictate that channel curvature and bed topography give rise to local perturbations in streamwise fluid velocity, prompting the preferential erosion and sediment deposition that constitute meander behaviour. Novel mathematical conditions are presented to guarantee unique solutions for the linearized equations in non-periodic domains with finite boundaries. With the boundary condition specification sufficient for the uniqueness proof one finds a well-posed initial-boundary-value problem amenable to standard numerical techniques for partial differential equations. This provides a pathway for improved numerical algorithms for simulations of meandering river dynamics. Previous theoretical analysis for linear stability theory in meandering dynamics has been restricted to spatially periodic systems. The present effort develops new results for linear stability theory in non-periodic systems with temporal driving at system boundaries as well as non-homogeneous initial conditions. Predictions for temporal driving at the inlets for non-periodic finite domains provide clarification for observed behaviour in laboratory flumes where driven conditions at the inlet avoids the long-term decay of all meanders observed in flumes with fixed entry conditions. Linear stability theory for finite domains confirms that a continuous perturbation is required for sustained meandering. Original scaling arguments are presented for the dependence of the meander migration rate on geological parameters, showing that the rate of channel migration increases with increased width, downreach slope and bank erodibility, and decreases with increased volumetric flow rate.

  PublisherOA PDFDOI

• Response to “Comment on ‘A periodic grain consolidation model of porous media’” [Phys. Fluids 31, 109101 (2019)]

  Physics of Fluids · 2019-10-01

  article1st authorCorresponding

  First Page

  PublisherDOI

• Fluid Mechanics and Heat Transfer

  2018-10-01

  book1st authorCorresponding
  Publisher

• A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

  Journal of Computational Physics · 2017-10-04

  articleSenior authorCorresponding
  PublisherDOI

• Meandering river dynamics: finite-domain theory and driven boundary conditions

  AGU Fall Meeting Abstracts · 2015-12-01

  articleSenior author
  Publisher

• Meandering River Dynamics: Spatial and Temporal Wave Growth and Non-Periodic Wave Patterns

  AGU Fall Meeting Abstracts · 2014-12-01

  articleSenior author
  Publisher

• Multiphase flow in porous media

  Journal of Fluid Mechanics · 2013-07-30 · 46 citations

  articleOpen access1st authorCorresponding

  Abstract Multiphase flows in porous media represent fluid dynamics problems of great complexity involving a wide range of physical phenomena. These flows have attracted the attention of an impressive group of renowned researchers and have spawned a number of classic problems in fluid dynamics. These multiphase flows are perhaps best known for their importance in oil recovery from petroleum reservoirs, but they also find application in novel areas such as hydrofracturing for natural gas recovery. In a recent article, Zinchenko & Davis ( J. Fluid Mech. 2013, vol. 725, pp. 611–663) present computational simulations that break new ground in the study of emulsions flowing through porous media. These simulations provide sufficient scale to capture the disordered motion and complex break-up patterns of individual droplets while providing sufficient statistical samples for estimating meaningful macroscopic properties of technical interest.

  PublisherOA PDFDOI

• Orientation and microstructure in sheared Brownian suspensions of anisotropic dicolloidal particles

  arXiv (Cornell University) · 2012-07-21

  preprintOpen accessSenior author

  Orientation and microstructure are investigated in sheared Brownian suspensions of hard dicolloidal particles, with the dicolloids modeled as two fused spheres of varying radii and center to center separations. Two different particle shapes named homonuclear (aspect ratio 1.1) and fused-dumbbells (aspect ratio 1.5) were considered. Hydrodynamic interactions between the particles were computed with a modified lubrication model called Fast Lubrication Dynamics. Studies were conducted for a wide range of volume fractions between $0.3 \leq ϕ\leq 0.5$ and Pèclet numbers between $0 \leq Pe \leq 1000$. The microstructure was found to be disordered at all volume fractions, though signatures of weak string like ordering were evident particularly in $ϕ=0.5$ homonuclear suspensions at intermediate to high shear rates ($Pe$ in the range 10-100). Complex orientation behavior was observed as a function of shape, shear rates, and volume fractions. At very low shear rates, random orientation distribution was observed in all cases. At the highest shear rates, orientation distribution in suspensions of homonuclear particles exhibited a shift towards an alignment with the vorticity axis at all volume fractions, while in suspensions of fused-dumbbells it exhibited a shift away from the vorticity axis at low volume fractions and a negligible shift at higher volume fractions. The orientation behavior is further characterized by examining the orientation distribution in the velocity--gradient plane -- in this case an increased particle alignment with the velocity axis is generally observed with increasing volume fractions, but not universally with increasing shear rates. Mechanistic origins for the complex orientation behavior as a function of shear rate, volume fraction, and particle shape is described.

  PublisherOA PDFDOI

• Dynamics of the orientation behavior and its connection with rheology in sheared non-Brownian suspensions of anisotropic dicolloidal particles

  Journal of Rheology · 2011-04-20 · 12 citations

  articleSenior author

  The orientation, microstructure, and rheology in non-Brownian shear flow were studied for suspensions of dicolloidal particles using a novel particle mesh Ewald Stokesian dynamics algorithm for anisotropic particles. Four different particle shapes were studied with dicolloids modeled as the union of two intersecting spheres. Dynamic simulations were conducted for periodic systems of 1000 particles for volume fractions ϕ=0.05–0.55. The suspension microstructure was disordered for all particle shapes at 0≤ϕ≤0.50, with some systems showing ordered microstructure at ϕ=0.55. The viscosity in the disordered state was similar for all particle shapes at equal volume fraction. Negative first and second normal-stress differences were found for ϕ≤0.5, but positive values were observed for certain ordered systems at ϕ=0.55. Complex orientation behavior was observed as a function of volume fraction and particle shape. All particles showed an orientation shift toward the vorticity axis for ϕ≥0.10. Certain shapes showed a shift away from the vorticity axis for ϕ≤0.10. The high ϕ orientation dynamics were consistent with predictions based on the mobility tensor MωS relating the angular velocity to particle stresslet. The orientation dynamics were dominated by the second normal-stress difference. The shift away from the vorticity axis for small ϕ was induced by migration away from orientations with large orientation fluctuations.

  PublisherDOI

Recent grants

• Computational Study of Three Dimensional Concentrated Emulsions and Foams with Surfactant Effects

  NSF · $200k · 2007–2010

Frequent coauthors

• Qingjun Meng

  15 shared

• Gregory P. Muldowney

  6 shared

• P. Dimitrakopoulos

  University of Maryland, College Park

  5 shared

• R. E. Larson

  3 shared

• Amit Kumar

  Rajendra Institute of Medical Sciences

  3 shared

• C. Pozrikidis

  Amherst College

  3 shared

• D. R. GRAHAM

  University of Illinois Urbana-Champaign

  3 shared

• A. KUMAR

  2 shared

Awards & honors

• Stanley Corrsin Lectureship in Fluid Dynamics, Johns Hopkins…
• Prokasy Award for Excellence in Undergraduate Teaching, Coll…
• Presidential Young Investigator Award, National Science Foun…