A structured but non‐uniform Cartesian grid‐based model for the shallow water equations

In large‐scale shallow flow simulations, local high‐resolution predictions are often required in order to reduce the computational cost without losing the accuracy of the solution. This is normally achieved by solving the governing equations on grids refined only to those areas of interest. Grids with varying resolution can be generated by different approaches, e.g. nesting methods, patching algorithms and adaptive unstructured or quadtree gridding techniques. This work presents a new structured but non‐uniform Cartesian grid system as an alternative to the existing approaches to provide local high‐resolution mesh. On generating a structured but non‐uniform Cartesian grid, the whole computational domain is first discretized using a coarse background grid. Local refinement is then achieved by directly allocating a specific subdivision level to each background grid cell. The neighbour information is specified by simple mathematical relationships and no explicit storage is needed. Hence, the structured property of the uniform grid is maintained. After employing some simple interpolation formulae, the governing shallow water equations are solved using a second‐order finite volume Godunov‐type scheme in a similar way as that on a uniform grid. Copyright © 2010 John Wiley & Sons, Ltd.