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Monolithic Newton‐multigrid solution techniques for incompressible nonlinear flow models
Author(s) -
Damanik H.,
Hron J.,
Ouazzi A.,
Turek S.
Publication year - 2012
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.3656
Subject(s) - nonlinear system , multigrid method , discretization , compressibility , mathematics , incompressible flow , newton's method , non newtonian fluid , flow (mathematics) , mathematical optimization , mathematical analysis , mechanics , physics , geometry , partial differential equation , quantum mechanics
SUMMARY We present special Newton‐multigrid techniques for stationary incompressible nonlinear flow models discretized by the high order LBB‐stable Q 2 P 1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviors and also regarding different problem sizes and types of nonlinearity. Here, local pressure Schur complement techniques are presented as a generalization of the classical Vanka smoother. The discussed methodology is implemented for the well‐known flow around cylinder benchmark configuration for generalized Newtonian as well as non‐Newtonian flows including non‐isothermal, shear/pressure dependent and viscoelastic effects.Copyright © 2012 John Wiley & Sons, Ltd.