# Physical Sciences Division

Research Highlights

April 2014

## Several Faces of Physics Become One

### New multiscale model unifies physical laws of water flow to span all scales

The unified multiscale model developed at PNNL couples water transport equations in such a way that this one model can represent transport at both pore (top) and watershed (bottom) scales. Enlarge Image

**Results:** Water
moves through multifaceted physical boundaries. This poses a significant
challenge for scientists who must simulate water flow across many domains.
Scientists at Pacific Northwest National Laboratory (PNNL) conquered this
barrier by merging different physical laws. Their new approach can describe any
type of water flow in soils and the terrestrial ecosystem, in soil pores, streams,
lakes, rivers and oceans, and in mixed media of pores and solids for soil and
aquifer. The versatile properties of the new approach allow cross-domain simulation
of water flow at different scales. The research was published in the *Soil Science Society of America Journal*.

**Why It Matters:** From stream flow, to soil and
irrigation saturation, to underground aquifers, understanding how water travels
through many varied regions is important for understanding water cycling and
its effect on agriculture, water conservation, and climate changes. For
scientists, the challenge is simulating water's travels through many different
domains in ways that are efficient and effective. Soil is a complex system
consisting of large spaces (macropore) where water easily flows and small
spaces (micropore) where water drains and saturates slowly. Two different
domains mean different calculations for the physical trail. Simulation of pore-scale
water flow in soils is traditionally described by coupling Navier-Stokes
equations in macropore and Darcy's law in porous domain containing micropore,
and then repeating the calculations continuously at these interfaces. The
researchers in this paper developed a new approach to eliminate the repeated
calculations at the domain interfaces, significantly simplifying water flow
simulations for ecosystems.

**Methods:** A
multidisciplinary team at PNNL developed the unified
theory and unified multiscale model (UMSM) that simulates water flow at all
scales. The new set of coupled mathematical equations unifies the
Navier-Stokes equations and Darcy's law to describe water flow at different
scales and across different physical domains. The team performed extensive
numerical verifications to evaluate the new model under both saturated and
unsaturated conditions. Using water flow in a soil core from Rattlesnake
Mountain in south-central Washington State as an example, they validated the
new model. Their numerical and experimental validation confirmed that the
unified model performs the same as the Navier-Stokes equations where these
equations are applicable and becomes Darcy's law in porous media.

"By solving a single set of equations in all ecosystem components, UMSM presents a system-scale approach to analyze water cycling," said Dr. Chongxuan Liu, biogeochemist and corresponding author of the paper. "This approach will facilitate integration of ecosystem water flow in large, climate-scale modeling."

**What's Next? **UMSM directly simulates water flow across
scales and physical domains in soils and ecosystems. The PNNL researchers are now extending UMSM to
describe biogeochemical processes in soils and ecosystems that are coupled with
water flow.

**Acknowledgments**

**Sponsor:** This research was supported by the U.S. Department of Energy's
(DOE) Office of
Biological and Environmental Research through the Terrestrial
Ecosystem Science program.

**Research Team: **Chongxuan Liu, Vanessa L Bailey, Xiaofan Yang, Jianying Shang, and Yilin Fang,
PNNL.

**Research Area: **Subsurface Science,
Chemical
Sciences

**User
Facilities:** EMSL, a
DOE national scientific user facility located at PNNL

**Reference:** Yang X, C Liu,
J Shang, Y Fang, and VL Bailey. 2014. "A Unified
Multi-Scale Model for Pore-Scale Flow Simulations in Soils." *Soil Science Society of America Journal*
78(1):108-118. DOI: 10.2136/sssaj2013.05.0190