### The Corrected Operator Splitting Approach Applied to An Advection-Diffusion Problem.

K. Hvistendahl Karlsen, K. Brusdal, H. K. Dahle, S. Evje, and K.-A. Lie

Abstract: So-called corrected operator splitting methods are applied to a $1$-D scalar advection-diffusion equation of Buckley--Leverett 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 2-D equations by means of dimensional splitting, and we apply it to a Buckley--Leverett type problem including gravitational effects.

Paper:
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Title:
The corrected operator splitting approach applied to an advection-diffusion 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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