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Filtering non‐solenoidal modes in numerical solutions of incompressible flows
Author(s) -
Rider William J.
Publication year - 1998
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/(sici)1097-0363(19981015)28:5<789::aid-fld728>3.0.co;2-4
Subject(s) - solenoidal vector field , mathematics , vector field , compressibility , filter (signal processing) , projection method , projection (relational algebra) , navier–stokes equations , mathematical analysis , incompressible flow , vertex (graph theory) , divergence (linguistics) , operator (biology) , decoupling (probability) , poisson's equation , geometry , mathematical optimization , physics , mechanics , algorithm , dykstra's projection algorithm , computer science , philosophy , discrete mathematics , graph , linguistics , engineering , biochemistry , transcription factor , computer vision , control engineering , gene , repressor , chemistry
Solving the incompressible Navier–Stokes equations requires special care if the velocity field is not discretely divergence‐free. Approximate projection methods and many pressure Poisson equation methods fall into this category. The approximate projection operator does not dampen high frequency modes that represent a local decoupling of the velocity field. For robust behavior, filtering is necessary. This is especially true in two instances that were studied: long‐term integrations and large density jumps. Projection‐based filters and velocity‐based filters are derived and discussed. A cell‐centered velocity filter, in conjunction with a vertex‐projection filter, was found to be the most effective in the widest range of cases. © 1998 John Wiley & Sons, Ltd.