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NEWTON–GMRES ALGORITHM APPLIED TO COMPRESSIBLE FLOWS
Author(s) -
CHOQUET RÉMI,
ERHEL JOCELYNE
Publication year - 1996
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(19960730)23:2<177::aid-fld418>3.0.co;2-n
Subject(s) - generalized minimal residual method , jacobian matrix and determinant , discretization , mathematics , convergence (economics) , newton's method , linear system , compressibility , rate of convergence , algorithm , mathematical optimization , mathematical analysis , computer science , nonlinear system , physics , mechanics , computer network , channel (broadcasting) , quantum mechanics , economics , economic growth
This paper addresses the resolution of non‐linear problems arising from an implicit time discretization in CFD problems. We study the convergence of the Newton–GMRES algorithm with a Jacobian approximated by a finite difference scheme and with restarting in GMRES. In our numerical experiments we observe, as predicted by the theory, the impact of the matrix‐free approximations. A second‐order scheme clearly improves the convergence in the Newton process.