PNNL-13501 - Pacific Northwest National Laboratory

Study Control Number: PN98017/1263
Conservation Laws in Support of Reactive Transport
Janet B. Jones-Oliveira, Joseph S. Oliveira, Harold E. Trease
This project focused on the development of an applied mathematics capability to provide new and more accurate scalable,
parallel, computational methods, and grid technologies for solving the reaction-diffusion type equations that are required
for higher resolution of the concentration fronts in reactive transport modeling. Tracking and resolving moving fronts and
their multiscale characteristics are important for such multi-material problems as predicting the migration pattern of
contaminated groundwater (as it interacts with solid and/or porous material walls in the flow path), particle transport in a
human lung, transport of molecules through the cell wall, and modeling the propagation of transient local climate effects
that are closely coupled to topographic surface boundary effects imposed by complex terrain within a regional and/or
global climate context.
Project Description
This project provided computational and mathematical
physics support for the development of new analytical
methods, hybrid grid technologies, algorithms, and
numerical techniques for the solution of partial
differential equations (PDEs) that are relevant to all scales
of physical transport, fluid-solid interactions, moving
shock fronts, and molecular chemistry interactions. This
work will affect a variety of modeling areas including the
Hanford vadose zone, design of new combustion systems,
bioengineering, and atmospheric chemistry and global
change.
Approach
The focus of this project was to improve the level of
applied mathematics and computational mathematical
physics in the areas of temporal and spatial multiscale
analysis, fluid-solid interaction, conservation-law
mathematics, and invariant numerical discretization
methods using multidimensional, hybrid grid
generation/refinement. Improved capability is required to
form the basis of more accurate simulations, as well as
more scalable high-performance computer codes,
particularly in the area of reactive transport.
The transport of material from one location to another is a
central tenent of most environmental issues. These flows
can be of an unreacting material or, as is more common,
the flow can contain reacting species that change their
chemical identity, thus potentially changing the
characteristics of the flow. In reactive transport, there is
the added difficulty of multiphase flow, with chemical
pumping. A key issue in the reactive transport area that
112 FY 2000 Laboratory Directed Research and Development Annual Report
requires high resolution is the fluid-solid interaction
across media and modeling scales. However, underlying
all of these physical modeling issues is the absolute need
to model the geometry correctly. If the geometric
modeling of the physical space where the physics and
chemistry occurs is not accurate, the propagation of the
species will be wrong. Hence our emphasis on precise
gridding technology.
We determined that either a Free-Lagrange (FL) or an
Arbitrary L`agrangian-Eulerian (ALE) formulation on
hybrid structured/unstructured/stochastic grids with
adaptive mesh refinement is required to resolve problems
observed in numerical implementations, which have been
attributed to the geometry/mesh resolution and interaction
of the front with that of the nonlinear model components.
An additional complexity that front-tracking methods
must resolve correctly is to capture the oscillatory
behavior of some of the variables behind the advecting
front. Therefore, we worked to develop the capability to
model problems using full-physics/full-chemistry
FL/ALE technology with adaptive mesh refinement on
hybrid grids. Development of this technology and
approach is directly applicable to problems in
combustion, atmospheric, subsurface, and particulate-inlung
modeling.
Results and Accomplishments
A clearer understanding of the transition from the microscale
(chemistry), to the meso-scale (pore-scale), and to
the macro-scale (field response) is necessary to ultimately
obtain an accurate long time-scale, large spatial-scale
model. In order to tackle this cross-scale problem, we
initially approached it via pursuit of numerical/analytical