Despite becoming increasingly popular in many branches of computational physics, Jacobian-free Newton-Krylov (JFNK) methods have not become the approach of choice in the solution of the compressible Navier-Stokes equations for turbulent aerodynamic flows. To a degree, this is related to some subtle
NEWTON–GMRES ALGORITHM APPLIED TO COMPRESSIBLE FLOWS
✍ Scribed by RÉMI CHOQUET; JOCELYNE ERHEL
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 678 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
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.
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