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An exploration of the IGA method for efficient reservoir simulation
Novel numerical methods present exciting opportunities to improve the efficiency of reservoir simulators. Because potentially significant gains to computational speed and
accuracy may be obtained, it is worthwhile explore alternative computational algorithms
for both general and case-by-case application to the discretization of the equations of porous media flow, fluid-structure interaction, and/or production. In the present
work, the fairly new concept of isogeometric analysis (IGA) is evaluated for its suitability
to reservoir simulation via direct comparison with the industry standard finite difference (FD) method and 1st order standard finite element method (SFEM). To this end, two main studies are carried out to observe IGA’s performance with regards to geometrical modeling and ability to capture steep saturation fronts. The first study explores IGA’s ability to model complex reservoir geometries, observing L2 error convergence rates under a variety of refinement schemes. The numerical experimental setup includes an 'S' shaped line sink of varying curvature from which water is produced in a 2D homogenous domain. The accompanying study simplifies the domain to 1D, but adds in multiphase physics that traditionally introduce difficulties associated with modeling of a moving saturation front. Results overall demonstrate promise for the IGA method to be a particularly effective tool in handling geometrically difficult features while also managing typically challenging numerical phenomena.Petroleum and Geosystems Engineerin
A statistical shape model for deformable surface
This short paper presents a deformable surface registration scheme which is based on the statistical shape
modelling technique. The method consists of two major processing stages, model building and model
fitting. A statistical shape model is first built using a set of training data. Then the model is deformed and
matched to the new data by a modified iterative closest point (ICP) registration process. The proposed
method is tested on real 3-D facial data from BU-3DFE database. It is shown that proposed method can
achieve a reasonable result on surface registration, and can be used for patient position monitoring in
radiation therapy and potentially can be used for monitoring of the radiation therapy progress for head and
neck patients by analysis of facial articulation
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
We present a new multigrid scheme for solving the Poisson equation with
Dirichlet boundary conditions on a Cartesian grid with irregular domain
boundaries. This scheme was developed in the context of the Adaptive Mesh
Refinement (AMR) schemes based on a graded-octree data structure. The Poisson
equation is solved on a level-by-level basis, using a "one-way interface"
scheme in which boundary conditions are interpolated from the previous coarser
level solution. Such a scheme is particularly well suited for self-gravitating
astrophysical flows requiring an adaptive time stepping strategy. By
constructing a multigrid hierarchy covering the active cells of each AMR level,
we have designed a memory-efficient algorithm that can benefit fully from the
multigrid acceleration. We present a simple method for capturing the boundary
conditions across the multigrid hierarchy, based on a second-order accurate
reconstruction of the boundaries of the multigrid levels. In case of very
complex boundaries, small scale features become smaller than the discretization
cell size of coarse multigrid levels and convergence problems arise. We propose
a simple solution to address these issues. Using our scheme, the convergence
rate usually depends on the grid size for complex grids, but good linear
convergence is maintained. The proposed method was successfully implemented on
distributed memory architectures in the RAMSES code, for which we present and
discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of
Computational Physic
Local time steps for a finite volume scheme
We present a strategy for solving time-dependent problems on grids with local
refinements in time using different time steps in different regions of space.
We discuss and analyze two conservative approximations based on finite volume
with piecewise constant projections and domain decomposition techniques. Next
we present an iterative method for solving the composite-grid system that
reduces to solution of standard problems with standard time stepping on the
coarse and fine grids. At every step of the algorithm, conservativity is
ensured. Finally, numerical results illustrate the accuracy of the proposed
methods
A conjugate gradient method for the solution of the non-LTE line radiation transfer problem
This study concerns the fast and accurate solution of the line radiation
transfer problem, under non-LTE conditions. We propose and evaluate an
alternative iterative scheme to the classical ALI-Jacobi method, and to the
more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR)
schemes. Our study is indeed based on the application of a preconditioned
bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel
geometry and in the frame of the two-level atom model, with monochromatic
scattering, are discussed. Rates of convergence between the previously
mentioned iterative schemes are compared, as well as their respective timing
properties. The smoothing capability of the BiCG-P method is also demonstrated.Comment: Research note: 4 pages, 5 figures, accepted to A&
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