1. One Team: Relevant... Ready... Responsive... Reliable Basic Research Program Particle-Scale Distribution of Soil Moisture in Porous Media 20 September 2007 Dr. Chris Kees and Dr. Matthew Farthing Coastal and Hydraulics Laboratory

2. Purpose: To develop a multi-scale theoretical and computational model of variably saturated granular/porous media that will improve our ability to perform engineering-scale analyses. Results: Theoretical and computational frameworks for passing information between microscopic two-phase flow/particle systems to macroscopic variably saturated media. New constitutive models for macroscopic models and numerical multiscale models for macroscale engineering models. Payoff: Understanding the macroscopic structural, hydraulic, thermal, electromagnetic, and chemical properties of variably saturated soils will lead to improved ability to detect subsurface targets and features, to build structures, and to predict chemical species transport in soils Schedule & Cost Total $ 726K MILESTONES Prior FY07 FY08 FY09 Years Army 227 249 250 Other Initial Plan/Prep ($K) Particle Scale Theory Particle Scale Simulator Three-phase Theory Particle-Scale Distribution of Soil Moisture in Porous Materials Status: Basic 6.1 Particle-Scale Velocity and Pressure Computations Three-phase Simulator $726K Total Army Program Multiscale Theory Multiscale Simulator

3. What is the Problem? – We don’t understand the macroscopic structural, hydraulic, thermal, electromagnetic, and chemical properties of variably saturated soils. These properties affect our ability to detect subsurface targets and features, build structures, and predict chemical species transport in soils. What are the barriers to solving the problem? – Accurately measuring thermodynamic conjugate variables in physical experiments under dynamic conditions, as required for formulation of fundamentally sound constitutive relationships, is not possible. Quantities such as phase pressures, surface tension, fluid phase distribution, fluid phase kinetic and potential energies cannot be independently measured at the pore scale. Collaboration across ERDC, commercial firms and/or academia – Ernest Berney (GSL) - Physics of granular media Clint Willson (LSU), - Particle scale measurements Tim Kelley (NCSU) - Multilevel solvers analysis Clint Dawson(UT, Austin) – Finite element analysis High Fidelity Vessel Effects Project (CHL) Countermine phenomenology (GSL) Institute for Maneuverability and Terrain Physics (ITL) What is innovative about this work? The use of particle-scale continuum fluid mechanics simulations that explicitly model the separate phases and the fluid-water and fluid-solid interfaces. The coupling of those models to discrete element models of granular materials to facilitate multi-scale numerical modeling of these systems. What is your publication plan? FY07 - Mini-symposium on near surface air/water flow at U.S. National Congress on Computational Mechanics (July). FY08 - Advances in Water Resources FY09 - Journal of Computational Physics, Multiscale Modeling and Simulation (SIAM). Particle-Scale Distribution of Soil Moisture in Porous Materials How will you overcome these barriers? – Apply state-of- the-art computational methods to rigorous continuum thermo-mechanical models of the interaction of air and water phases in granular materials; collaborate with experimentalists and numerical analysis specialists from academia. What are the results of this research and what is its value? – A multiscale theoretical and computational modeling capability for variably saturated granular materials. The ability to calculate macroscopic properties from particle-scale measurements and/or use simulations to supplement experimental methods in complex three- dimensional settings where direct observation of all physical quantities is not possible; a computational multiscale framework that can be used to carry out fundamentally sound engineering analyses.

4. One Team: Relevant... Ready... Responsive... Reliable Accomplishments / Status Working prototype of 2D/3D air/water Navier-Stokes model based on front- capturing approaches. Working prototypes of 1D/2D/3D macro- scale (porous media) air/water flow models using locally mass-conservative continuous and discontinuous finite element methods. Set up five month visit to UT by Kees to collaborate with various researchers on numerical and pore-/multi-scale modeling issues.

5. One Team: Relevant... Ready... Responsive... Reliable Accomplishments / Status

6. One Team: Relevant... Ready... Responsive... Reliable Accomplishments / Status

7. One Team: Relevant... Ready... Responsive... Reliable Accomplishments / Status Cross-section of a 3D tomographic image showing residual water (blue), air (red), sand (green). Courtesy of Clint Willson, LSU.

8. One Team: Relevant... Ready... Responsive... Reliable Theoretical and computational frameworks for passing information between microscopic two-phase flow/particle systems to macroscopic variably saturated media. New constitutive models for macroscopic models and numerical multiscale models for macroscale engineering models. Products

9. One Team: Relevant... Ready... Responsive... Reliable High-fidelity vessel effects(Kees and Farthing): Arbitrary Lagrangian-Eulerian mesh technology and porous structure theory/models. Countermine Phenomenology(Howington): Mesh generation capability and moisture distribution theory/models. Stress Transfer in Granular Media(Peters):Discrete Element method coupling and upscaling tools, surface tension theory/models. Technology Transfer

10. One Team: Relevant... Ready... Responsive... Reliable USNCCM 2007 Minisymposium –Robust Nonlinear Iterative Methods for Time-Dependent Unsaturated Flow. Kees, Farthing, et al. –Locally Conservative, Stabilized Finite Element Methods for Richards’ Equation. Farthing, Kees, et al. –A Computational Tool for Creating Synthetic, Smallscale Infrared Imagery of Vegetated Soil Surfaces. Peters, Ballard, et al. Locally Conservative, Stabilized Finite Element Methods for Richards’ Equation. Kees, Farthing, et al. To be Submitted 10/07 Computational Geosciences Local Discontinuous Galerkin Approximations to Richards’ Equation. Li, Farthing, et al. Advances in Water Resources 30, 555-575 (2007). Adaptive Local Discontinuous Galerkin Approximations to Richards’ Equation. Li, Farthing, et al. Advances in Water Resources 30, 1883-1901. (2007). Publications and Related Work

11. One Team: Relevant... Ready... Responsive... Reliable A numerical model of particle-scale two- phase flow. A theory of variably-saturated granular media. A numerical model of variably-saturated granular media A multi-scale theoretical and computational model of variably-saturated granular media. Publications

12. One Team: Relevant... Ready... Responsive... Reliable Porous media experiments –Clint Willson (LSU) –David DiCarlo (UT) –Tissa Illangesekare (CSM) Mesh generation –Graham Carey (UT) –Owen Eslinger (ITL) Finite Elements –Clint Dawson (UT) –Lea Jenkins and John Chrispell (Clemson) Pore-scale and Multi-scale Theory and Computations –Steve Bryant and Masa Prodanovic (UT) –Todd Arbogast (UT) Collaborations

13. One Team: Relevant... Ready... Responsive... Reliable Research on physical theory is related to thin film research in industrial mathematics, non-aqueous phase liquid research in environmental engineering, and granular media research in civil engineering. Combining fluid mechanics with solid mechanics is an active area in several fields, but no consensus on a standard set of theoretical or computational tools exists. Assessment of Research Area

14. One Team: Relevant... Ready... Responsive... Reliable Issues Weak points in the computational infrastructure –Mesh generation –Visualization –Stability, maturity, availability of HPC environment –Fast, robust solvers for parallel architectures Weak points in the theoretical approach –Non-equilibrium thermodynamics. –Obtaining relevant experimental data and incorporating into the models. –Accurately modeling the stress jump due to surface tension and conservation of mechanical energy and mass