Preprint 1996-001

Dimensional Splitting with Front Tracking and Adaptive Grid Refinement

Abstract: Front tracking in combination with dimensional splitting is analysed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that \emph{surprisingly} high CFL numbers (typically in the range 5--15) can be used without loss of accuracy. A new method for grid refinement is introduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each grid cell as a criterion for introducing new or removing existing refinements. Several numerical examples are included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations.

Paper:

Revised version available as PostScript

Title:

Dimensional Splitting with Front Tracking and Adaptive Grid Refinement

Author(s):

Knut-Andreas Lie, mailto:andreas@math.ntnu.no

Vidar Haugse mailto:vidarh@ipt.unit.no,

Kenneth Hvistendahl Karlsen, mailto:kennethk@mi.uib.no

Publishing information:

Preprint. Mathematics No. 2/1996,ISSN: 0804-029X.
Norwegian University of Science and Technology, Trondheim, Norway.

Comments:

The paper has been revised February 19 1997.

Submitted by:

mailto:andreas@math.ntnu.no June 10 1996.