Dimensional splitting with front tracking and adaptive grid refinement

✍ Scribed by K.-A. Lie; V. Haugse; K. Hvistendahl Karlsen

• Book ID: 102657188
• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 584 KB
• Volume: 14
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199809)14:5<627::aid-num6>3.0.co;2-k

✦ Synopsis

Front tracking in combination with dimensional splitting is analyzed 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 large CFL numbers can be used without loss of accuracy for a wide range of problems. 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.