PNNL-13501 - Pacific Northwest National Laboratory

Figure 1. X3DGEN tetrahedral mesh of SST S-SX
stratigraphic data (provided by Bruce Williams) for
Handford Site wells W22-39, W22-44, W22-45, W22-46,
W23-13, W23-14, and W23-15. Note the numerous
geologically induced geometric pinch points in the threedimensional
volume.
methods for solving the fundamental physical
conservation laws. Such a hybrid approach was highly
successful in linearized, but fully coupled, fluid-solid
interaction modeling using special functions and power
series expansion arguments. In FY 1998, we
experimented with numerical homogenization of
nonlinear ordinary differential equations (ODEs). The
idea was to use wavelet homogenization methods for a
given system of nonlinear ODEs so that, for a given
tolerance, the algorithm would derive a numerical
solution that captures a coarse-scale solution with just
enough resolution such that the averaged contribution
from the fine-scale would be within acceptable tolerance.
This work was continued in FY 1999; however, the
wavelet method did not turn out to be as promising as we
had hoped.
We decided to apply the unstructured mesh technology to
model the pore-scale physics, with the aim of capturing
the geometry as precisely as possible, thereby hoping to
capture the subgrid scale physics more exactly, in order to
gain insight into what information can and must cross
scales. We initiated work with Dr. George Zyvoloski at
Los Alamos National Laboratory, and Dr. Tom Russell at
University of Colorado in this regard. Further, we began
working with Dr. Harold Trease, then at LANL to
incorporate into the computer code X3D (a) the fluid-solid
interaction capability, i.e., to build in a mechanism to
(a) X3D is a full-physics, first principles, time-domain code
that was designed at LANL for parallel processing on
unstructured grids. Its principal author is Dr. Harold E. Trease,
who developed the code based upon his dissertation in Free-
Lagrange methods.
define the compatability conditions across the fluid-solid
interface and optimize the dynamics modeling in two
acoustic impedance mismatched materials.
In FY 1999, our modeling efforts were directed primarily
in two areas: 1) bringing to PNNL new computational
capabilities, to address similar physical problems using
alternative methods that may be more suitable for
compressible flow and reactive transport, including
subgrid modeling, Free-Lagrangian and ALE methods
with adaptive mesh refinement; and 2) determining
example problems to test the strengths and weakness of
the structured versus the unstructured mesh approaches.
We obtained serial versions of Lawrence Livermore
National Laboratory’s DYNA3D (b) , NIKE3D (c) , and
ALE3D (d) with the understanding that parallel versions of
some subroutines could be made available on an
Figure 2. X3D unstructured global grid with adaptive mesh
refinement, which is driven by steep gradients in the
vorticity, S. When the ratio of the vorticity to its gradient is
> 1, the mesh is refined. When this ratio is < 1, the mesh
density is coarsened.
(b) DYNA3D is a nonlinear, explicit, 3-D finite element code for
solid and structural mechanics, which was originated by
Dr. John O. Hallquist while at LLNL.
(c) NIKE3D is a nonlinear, implicit, 3-D finite element code for
solid and structural mechanics, which also was originated by
Dr. John O. Hallquist while at LLNL.
(d) ALE3D is an arbitrary Lagrange/Eulerian, 3-D
hydrodynamics code with material strength, which was
developed to model the behavior of objects undergoing gross
deformation due to the application of shocks in the kilobar
regime. ALE3D employs arbitrarily connected hexahedral
calculational elements and has slide surfaces. The ALE
algorithm is implemented by carrying out a complete
Lagrangian calculation followed by an advection step.
Computational Science and Engineering 113