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A mass‐conservative staggered immersed boundary model for solving the shallow water equations on complex geometries
Author(s) -
Canestrelli Alberto,
Spruyt Aukje,
Jagers Bert,
Slingerland Rudy,
Borsboom Mart
Publication year - 2015
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.4180
Subject(s) - curvilinear coordinates , shallow water equations , solver , cartesian coordinate system , immersed boundary method , grid , boundary (topology) , boundary value problem , mathematics , momentum (technical analysis) , mathematical analysis , geometry , mathematical optimization , finance , economics
Summary In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut‐cell/ghost‐cell method is used together with a direction‐splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second‐order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd.