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A symmetry preserving dissipative artificial viscosity in r ‐ z geometry
Author(s) -
Váchal Pavel,
Wendroff Burton
Publication year - 2014
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.3926
Subject(s) - dissipative system , geometry , symmetry (geometry) , viscosity , grid , circular symmetry , tensor (intrinsic definition) , mathematics , polar , physics , classical mechanics , rotational symmetry , mathematical analysis , quantum mechanics , astronomy
SUMMARY We present a novel artificial viscosity for staggered Lagrangian schemes in 2D axi‐symmetric r ‐ z geometry on logically rectangular grids. The suggested viscous force is dissipative by construction, conserves both components of momentum, and preserves spherical symmetry on an equiangular polar grid. This method turns out to be robust and performs well for spherically symmetric problems on various grid types (symmetric, perturbed polar, rectangular), without any need for tinkering with problem‐dependent or grid‐dependent parameters. The results are compared with the outcome of the area‐weighted approach using the popular tensor viscosity by Campbell and Shashkov. Copyright © 2014 John Wiley & Sons, Ltd.