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A unified sub‐cell force‐based discretization for cell‐centered Lagrangian hydrodynamics on polygonal grids
Author(s) -
Maire PierreHenri
Publication year - 2011
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.2328
Subject(s) - discretization , lagrangian , solver , mathematics , robustness (evolution) , formalism (music) , classical mechanics , mathematical analysis , mathematical optimization , physics , art , biochemistry , chemistry , musical , visual arts , gene
We develop a general formalism to derive cell‐centered Lagrangian scheme, wherein numerical fluxes are expressed in terms of sub‐cell force. The general form of the sub‐cell force is obtained by requiring the scheme to satisfy a semi‐discrete entropy inequality. Sub‐cell force and nodal velocity are computed consistently with cell volume variation by means of a node‐centered solver, which results from total energy conservation. Numerical results demonstrate the accuracy and the robustness of this scheme. Copyright © 2010 John Wiley & Sons, Ltd.