Jean-Paul Mogou Dessap's thesis
by
Jean-Paul Mogou Dessap, M.S.E.
University of Texas at Austin, 1995
Supervisor: Kamy Sepehrnoori
The Laplace transform finite-difference (LTFD) method is a numerical technique
that solves partial differential equations (PDEs) by applying the Laplace
transformation to the PDEs, solving the resulting equations using finite-difference
methods and subsequently applying an inverse numerical transformation to obtain the
solution. Since the Laplace transformation is applied with respect to time, there is
no time discretization and all drawbacks arising from it (time truncation error,
roundoff error due to time discretization, and stability problems) vanish, yielding
a more accurate solution, achieved in less computer time than when a traditional
finite-difference scheme is used.
We applied the LTFD method to a one-dimensional (1D) convection-diffusion (CD)
equation in order to perform a thorough comparison with a traditional
finite-difference scheme. The improvements in terms of computer time and accuracy
were assessed. Three Laplace inversion algorithms were carefully examined. The
conditions of their applicability and the optimal choice of their parameters were
determined.
Next, the LTFD was implemented in the Sandia Waste-Isolation Flow and Transport
(SWIFT II) simulator. SWIFT II is a three-dimensional (3D) finite-difference code
used to simulate flow and transport processes in geologic media which may be
fractured. The LTFD implementation was performed for steady-state flow conditions
on the radionuclide transport equation as well as the waste-leach and dual-porosity
submodels. The mass balance calculations were also performed in the Laplace space.
In addition, a higher-order finite-difference scheme was implemented in SWIFT II to
discretize the convection term of the conservation equations. This allowed additional
improvements in the numerical solutions.
The tremendous improvements observed in solving the 1D convection-diffusion equation
were also confirmed in the SWIFT II implementation. The reduction in execution time
is impressive, especially for evaluations of nuclear-waste repositories when the
time frame of interest may extend over many thousands of years. The LTFD version of
SWIFT II is several folds faster and more accurate than the original SWIFT II for
the simulations carried out in this work.
Back to theses index
