A Structured but NonUniform Cartesian Grid Based Model for the Shallow Water Equations
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 Professor Qiuhua Liang




Author(s)   Liang Q 
Publication type   Article 
Journal   International Journal for Numerical Methods in Fluids 
Year   2011 
Volume   66 
Issue   5 
Pages   537–554 
ISSN (print)   02712091 
ISSN (electronic)   10970363 



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In largescale shallow flow simulations, local highresolution 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 nonuniform Cartesian grid system as an alternative to the existing approaches to provide local highresolution mesh. On generating a structured but nonuniform 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 secondorder finite volume Godunovtype scheme in a similar way as that on a uniform grid. 



Publisher   John Wiley & Sons Ltd. 
URL   http://dx.doi.org/10.1002/fld.2266 
DOI   10.1002/fld.2266 

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