An accurate multidimensional limiter on quadtree grids for shallow water flow simulation

ABSTRACT

In hydraulic research, numerical modelling of complex flows is essential for managing water risks. High-resolution finite volume schemes have become popular for shallow water flow modelling due to their mass and momentum balance characteristics and their ability to capture shocks. These methods use slope limiters to suppress numerical oscillations near discontinuities. However, one-dimensional limiters do not assure numerical accuracy in multidimensional applications, occasionally leading to excessive or insufficient numerical dissipation. For this reason, a multidimensional limiting process (MLP) was developed for oscillation control in multidimensional compressible flows. In this paper, we implement MLP on adaptive quadtree grids for shallow water flow simulations and compare MLP performance with simulations using conventional limiters. Four simulation cases show that MLP outperforms conventional limiters, and yield more accurate and stable solutions on adaptive quadtree grids. The capability of MLP for oscillation control is more noticeable on quadtree than on uniform grids.

Keywords:

• Finite volume model
• multidimensional limiting process
• quadtree grid
• shallow water flow
• slope limiter

Acknowledgements

We would like to express our appreciation to the developer of Gerris, Stephane Popinet, and thank anonymous reviewers for providing us with constructive comments and suggestions.

Funding

This work was partly supported by a grant from a Strategic Research Project funded by the Korea Institute of Construction Technology and by the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2013-C3-031).