Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique Page: 14 of 47
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The code has been built on top of the SAMRAI (Structured Adaptive Mesh Refinement)
Hornung and Kohn (2002) library developed at LLNL. SAMRAI is a general object-oriented
software infrastructure for implementing parallel scientific applications that employ structured
adaptive mesh refinement. The method uses a hierarchical structured grid approach first devel-
oped by Berger and Oliger (1984). In particular, AMR is based on a sequence of nested grids
with successfully finer spacing in both time and space. Increasingly finer grids are recursively em-
bedded in coarse grids until the solution is sufficiently resolved. An error estimation procedure
evaluates where additional refinement is needed and grid generation procedures dynamically
create or remove rectangular fine grid patches as resolution requirement change (Figures 1, 15).
Automatic regridding in time is based on Richardson extrapolation and in space on detection
of gradients (velocity, scalar etc) in the solution. SAMRAI provides the backbone of our imple-
mentation, managing the locally-refined Cartesian grid patch hierarchy with both the Eulerian
and Lagrangian data points defined on the hierarchy. It also provides facilities for performing
adaptive regridding, load balancing, and parallel data communication. To store and manage
the Lagrangian data points a version of the SAMRAI IndexData patch data type is used. For
a general-purpose solver library, we have chosen PETSc Balay et al. (2004), developed at Ar-
gonne National Laboratory. This suite solves large-scale linear and nonlinear equations. We
used preconditioned Krylov methods provided by this library. A parallel data managing and
implementation is done similar to algorithm described in Griffith et al. (2001).
3 Validation against empirical data and experiments
3.1 Fixed particle beds
Flow behavior through packed beds of spheres or other porous-media-like structures are of
crucial importance in industry and nature. The determination of pressure drop through a packed
bed as a function of fluid flow rate, geometrical constrains of the bed and physical properties of
bed material is very critical, for example, in hydraulic and pneumatic devices. The well-known
empirically derived equation used for that purpose has been proposed by Ergun (Ergun, 1952)
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Kanarska, Y; Lomov, I & Antoun, T. Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique, article, September 10, 2010; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc868095/m1/14/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.