Mike Sukop: Research

 

Our research is focused on environmental computational fluid dynamics in geometrically complex domains such as cityscapes, natural and engineered surface water bodies, and cavernous, fractured, and porous media. Solute and heat transport in these complex media and their simulation, including inverse modeling, are key interests.

 

This research is done at a broad range of scales using both traditional and lattice Boltzmann models. Single and multi-phase lattice Boltzmann models figure prominently in research aimed at better methods for solute transport in karst and fractured aquifers, and for water and nonaqueous fluid behavior in fractured and porous media – especially partially saturated media.

 

I maintain ongoing interests in fractals, multifractals, cellular automata, percolation phenomena, geostatistics, and surface chemistry and their applications.

 

My former post-doc Danny Thorne and I wrote an introductory book  summarizing our first few years of learning about LBM: Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Our Lattice Boltzmann code LB2D_Prime is sort of a companion to the book and does many different types of simulations. Katie Bardsley has produced a User's Guide.

 

Relatively recent work has been focused on building a density-dependent Darcy's Law/anisotropic dispersion solver comparable to standard ground water flow/transport models but retaining the tremendous advantage of being able to solve higher Reynolds number flows and transport (governed by eddy diffusion) in larger open spaces in a tightly coupled way. Here is an example:

 

 

Here are some (2-D) examples of wind carrying a tracer through lidar-sampled urban canyons of downtown Miami:

 

 

                                                           

 

 

 

 

 

Here are examples of (periodic) Poiseuille flows perturbed by a square obstacle at 2 different Reynolds numbers:

 

 

 

 

Here is an example of some work on density-driven flows. We aim to demonstrate our ability to solve some of the classic benchmark problems so that we can justify applying our methods to saltwater intrusion problems. We have a promising start working on the 'Elder Problem'.

 

                                                        

 

We are getting excellent agreement with classic experiments at different Reynolds numbers. Of course, we can simulate flows in any geometry quite easily and probably important things like entry length effects are properly accounted for. I think the ability to handle such flows will be important for simulating karst aquifers. Solute transport is closely coupled with the fluid simulations. Here are some examples for schematic karst domains at different Re.

 

            

 

Here is a shallow water equation simulation we did for a proposal to compare LBM to standard engineering methods for flow through culverts and bridges. 

 

The focus of my postdoctoral research with Dani Or was single component multiphase models and their application to unsaturated porous media. Although a great deal has been done on 2 component multiphase systems, which simulate for example oil and water, much less has been done with single component systems which intend to simulate a material that can exist in liquid and vapor forms – like water and its vapor.

 

Our work is proving these models to be exceptionally versatile, and many problems that have long defied quantitative treatment can now be examined. Simultaneous liquid and vapor flow, variable surface wettability, high Reynolds number flows, evaporation/condensation, cavitation, gravitational forcing, and arbitrarily complex geometry can all be readily simulated.

 

Here are some movies that show variable wettability of solid surfaces. These simulations show surfaces that range from completely wettable to non-wetting. Each simulation begins with a liquid drop adjacent to one side of a box.

 

               

 

We are also looking at adsorption/capillary condensation phenomena. Below, I’ve placed movies of simulations in slits with different vapor pressures (densities) applied at the ends.

r_vap=85.7 r_vap=85.7857  r_vap=86.1285r_vap=86.557

 

I have also worked on the hysteretic drainage and filling of angular pores. Here is an example:

The pore fills and drains ‘catastrophically’ at different vapor pressures.

 

We’ve done some simulations on drainage of model 2-D porous media in the context of invasion percolation theory and the importance of the Capillary number and geometrical details of the medium. Here’s a movie where the solids are white, dark blue is liquid, and light blue is vapor:

 

 

If we add gravity, the drainage process is stabilized:

 

 

Here is a drop falling from a slit. There are complicated compressibility issues that result from a ‘bad’ equation of state (EOS) and add some features that are unrealistic for water, but are probably roughly correct for the fictional fluids that correspond to this particular EOS. 

 

 

You can find some additional simulations here and in my Presentations.