Preprint 1998002
The Corrected Operator Splitting Approach Applied to An
AdvectionDiffusion Problem.
K. Hvistendahl Karlsen, K. Brusdal, H. K. Dahle, S. Evje, and
K.A. Lie
Abstract:
Socalled corrected operator splitting methods are applied to a $1$D
scalar advectiondiffusion equation of BuckleyLeverett type with
\textit{general} initial data. Front tracking and a \textit{$2$nd} order
Godunov method are used to advance the solution in time. Diffusion is
modelled by piecewise linear finite elements at each new time level. To
obtain correct structure of shock fronts independently of the size of the
time step, a \textit{dynamically defined} residual flux term is grouped
with diffusion. Different test problems are considered, and the methods
are compared with respect to accuracy and runtime. Finally, we extend the
corrected operator splitting to 2D equations by means of dimensional
splitting, and we apply it to a BuckleyLeverett type problem including
gravitational effects.
 Paper:
 Available as PostScript (3.0 Mbytes) or
gzipped PostScript (720 Kbytes; uncompress
using gunzip).
 Title:
 The corrected operator splitting approach applied to an
advectiondiffusion problem.
 Author(s):
 K. Hvistendahl Karlsen,
<kenneth.karlsen@mi.uib.no>
 K. Brusdal,
<kari.brusdal@mi.uib.no>
 Helge K. Dahle,
<helge.dahle@mi.uib.no>
 S. Evje,
<steinar.evje@mi.uib.no>
 K.A. Lie,
<andreas@math.ntnu.no>
 Publishing information:
 To appear in Comput. Methods Appl. Mech. Engrg.
 Comments:

 Submitted by:

<kenneth.karlsen@mi.uib.no>
January 16 1998.
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