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I'm looking for a comparison between the Jacobian-Free Newton-Krylov (JFNK) method performance compared to the conventional CFD nonlinear solution methodologies like SIMPLE.

Does anyone know if such a document exists? Also, if anyone has any intuition on this without any direct evidence, I would like to hear about it.

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  • $\begingroup$ See, for instance, D.A. Knoll, D.E. Keyes, Jacobian-free Newton–Krylov methods: a survey of approaches and applications//Journal of Computational Physics 193 (2004) 357–397 $\endgroup$ Jun 9 at 10:01

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Below is a similar case in which a coupled method is compared with a SIMPLE-like segregated one. The author showed an impressive acceleration of convergence.

Darwish I. et al., A Coupled Incompressible Flow Solver on Structured Grids. Numerical Heat Transfer, 52, 2007(4).

Coupled N-S solver

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