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Simple treatment of non‐aligned boundaries in a Cartesian grid shallow flow model
Author(s) -
Liang Qiuhua,
Borthwick Alistair G. L.
Publication year - 2007
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1615
Subject(s) - shallow water equations , grid , hydraulic jump , solver , geometry , cartesian coordinate system , boundary (topology) , discretization , boundary value problem , mesh generation , flow (mathematics) , waves and shallow water , regular grid , simple (philosophy) , geology , interpolation (computer graphics) , conformal map , computer science , mathematics , mathematical analysis , mathematical optimization , engineering , structural engineering , computer graphics (images) , animation , philosophy , oceanography , epistemology , finite element method
A simple method is proposed for treating curved or irregular boundaries in Cartesian grid shallow flow models. It directly evaluates fictional values in ‘ghost’ cells adjacent to boundary cells and requires no interpolation or generation of cut cells. The boundary treatment is implemented in a dynamically adaptive quadtree grid‐based solver of the hyperbolic shallow water equations and validated against several test cases with analytical or alternative numerical solutions. The method is easy to code, accurate, and demonstrably effective in dealing with irregular computational domains in shallow flow simulations. Results are presented for still water in a basin of complicated geometry, steady hydraulic jump in an open channel with a converging sidewall, wind‐induced circulation in a circular shallow lake, and shock wave diffraction in a channel containing a contraction and expansion. Copyright © 2007 John Wiley & Sons, Ltd.