A Review of Solution Stabilization Techniques for RANS CFD Solvers

Round 1

Reviewer 1 Report

The paper is a nicely written overview paper.

Maybe one could cite the following paper:

Gomes, Pedro, and Rafael Palacios. "Pitfalls of discrete adjoint fixed-points based on algorithmic differentiation." AIAA Journal 60.2 (2022): 1251-1256.
https://arc.aiaa.org/doi/pdf/10.2514/1.J060735

There one finds nicely presented GMRES results.

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Reviewer 2 Report

 

 

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Reviewer 3 Report

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Round 2

Reviewer 2 Report

First of all, I would like to congratulate the authors for the effort carried out to present this revised paper. The work done to improve the quality of the paper is impressive.

Nevertheless, I would have minor remarks to express.

- ref 4 and ref 55 are the same.

- introduction l47: rpm in upper cases is more coherent with the rest of the paper

- the RPM method is clearly presented. But I think that the key point is the determination of the eigen vectors. The authors may explain a little bit more the way these vectors are determined efficiently

- Fig 3: the curve titled "GMRES" is not mentioned in the explanation of the figure

-line 410 "superior robustness": Be carefull with the term robustness. The Newton method is robust only if the guess solution is close enough the final solution. Otherwise the algorithm diverges.

line 456: I think that the theoretical aspect of the GMRES is out of the scope of this paper. A simple reference to the Saad's works is enough, since the paper is focused on the resolution of the non-linear systems. The presented algorithms uses the GMRES one. Current reseaches are performed on the GMRES to improve its accuracy (flexible gmres, preconditioned GMRES, GMRES preconditioned with another GMRES, ...). The key point is the preconditioning.

- Algorithm 1: it is not the modified Gram-Smidt that is pesented but the classical Gram-Schmidt. It is unuseful to present the algorithm in the paper.

-l 517: very interesting and important remark

-eq 72: the presented law of evolution of the Courant number is a smooth one. More "aggressive" laws have been used and yield much quicker convergences.

-l 720: there si a debate on the the way to consider the turbulent variables. when using an implicit scheme, decoupling the turbulent equations from the conservative ones seems to be more efficient than considering the set of 6 or 7 coupled equations. This is not necessary the case when using a NK or an ANK algorithm

subpart 3.5.2: I think that a review paper must cite 2 papers about the convergence acceleration of TSM solvers.  "Block-Jacobi Implicit Algorithms for the Time Spectral Method", F. Sicot, G. Puigt M. Montagnac, AIAA Journal vol 46 dec 2008 (one of the first paper presenting an implicit resolution of the TSM)

"Toward an optimal solver for the time-spectral fluid-dynamic and aeroelastic solutions on unstructered meshes", N. L. Mundis, D. J. Mavriplis, Journal of Computational Physics 345 pp 132-161, 2017 (one of the first presenting a robust resolution independent of the number of time instants)

I recommend the publication of this paper after minor modifications

 

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