Multidomain Modeling for the Simulation of Flow and Transport in a Neighborhood of an Underground Nuclear Waste Repository
Creators: name: Sboui, Amel
name: Clement, Francois
name: Jaffre, Jerome
name: Kern, Michel
name: Martin, Vincent
name: Roberts, Jean
name: Sboui, Amel
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: In this presentation we are concerned with the problem of developing a numerical
simulator for modeling flow and contaminant transport in the vicinity of an
underground nuclear waste repository for use in performance assessment.  Clearly
reasonably accurate and reliable simulators are needed, but as performance assessment
requires many simulations, it is also important that the simulators be very
efficient.   The simulations under consideration necessarily involve large scale
calculations both in space and in time, and yet must take into account important
heterogeneities in the domain.
This suggests the use of multidomain modeling:  the domain is divided into more
nearly homogeneous subdomains and efficient numerical solvers are used for each
subdomain.
The calculations on the various subdomains are related through transmission or
interface conditions, and parallel computing and high level programming languages can
then be used for numerical implementation.

Around the waste depository the porous medium is made up of several regions of
different permeability, the permeability  varying over several orders of magnitude
from one region to the next.  In the method developed  here
 the domain is partitioned into homogeneous subdomains and  nonoverlapping domain
decomposition is used for both the flow calculations and to solve the transport
equation.  

The single phase flow equation is an elliptic equation coupling a conservation
equation with Darcy's law.
 As the Darcy velocity is the unknown of interest, a mixed finite element method is
used to solve the equation within the subdomains.  
 In order to be able to use general hexahedral grids, Kuznetsov-Repin macroelements
are used.
 Continuity of the pressure and continuity of the flux are enforced at the interfaces
between the subdomains using a balancing domain decomposition method.
 This method has the advantage of being very robust with respect to large contrasts
in permeability.

The transport equation is of advection-diffusion type.  To approximate the solution
to this equation an operator splitting technique is used:   an advection equation is
solved alternately with a diffusion-dispersion-decay equation. The parabolic
diffusion-dispersion-decay equation is solved implicitly using mixed finite elements
while the advection equation is solved explicitly using cell centered finite volumes
with upstream weighting.  In this way we are able to use a smaller time step for the
advection equation when the advection coefficient is large.    The domain
decomposition methods used for the pressure equation extend also to these time
dependent problems.  

In subdomains of high permeability, the natural time scale is much more rapid than in
neighboring subdomains with lower permeability, and a much smaller time step size
must be used for the advection step is these subdomains.   However if only one time
step size is used for all of the advection steps, it is the more rapid time scale
that is imposed and the much smaller time step size must be used throughout the
domain even if the size of the region in which it is required is relatively small.
This suggests the use of different time step sizes for different subdomains.

One of the many advantages of using domain decomposition techniques is that they lend
themselves readily to parallelization.  
However, implementing the subdomain coupling requires complex programming.  This is
done efficiently using the programming environment OCamlP3l.  This is a recently
developed part of the strongly typed functional programming language OCaml which can
be used for parallel computing.

Realistic  three dimensional numerical experiments from the Andra project will be shown.