On the Development of an Implicit Discontinuous Galerkin Solver for Turbulent Real Gas Flows
, Antonio Ghidoni 1,*, Gianmaria Noventa 1, David Pasquale 3 and Stefano Rebay 1Round 1
Reviewer 1 Report
An implicit discontinuous Galerkin fluid dynamic solver is developed in this work for turbulent real gas flows. The real gas thermodynamic models, such as Peng-Robinson and van der Walls model and Span-Wagner model, are used. Moreover, the automatic differentiation is performed to obtain the exact Jacobian matrices. The topic is interesting. Here are detailed comments.
1) 2.3. Temporal discretization, for the Eq. (17), the superscript “n” is the time step index. Therefore, I guess the Eq. (17) is only solved once in each time. It means only one Newton iteration is performed in each time step. Is it right?
2) GMRES solver is used to solve the linear equation. It is well known that the preconditioning technology is a key issue for the GMRES solver to ensure its efficiency. Please discuss the choice of the preconditioner in this work.
3) In this work, the automatic differentiation is used to compute the exact Jacobian matrix. Actually, the finite difference is another widely-used method to calculate the Jacobian matrix automatically. For example, “Finite difference Jacobian based Newton-Krylov coupling method for solving multi-physics nonlinear system of nuclear reactor”. Please briefly review and discuss the features and difference between these two methods.
4) For the compressible flow, especially the high Mach flow with shock, some special treatments should be considered to model the compressible effect. Please discuss how to consider the compressible effect in the turbulent model.
5) Please discuss the effectiveness of turbulent model near the wall for the wall-type boundaries.
6) Newton-Krylov method is a powerful nonlinear solver and has been widely used in varied engineering communities. Please briefly review the recent development of Newton-Krylov method and its variants. Here are some examples which may useful. [1] A Jacobian-free approximate Newton–Krylov startup strategy for RANS simulations, 2019 [2] An assessment of coupling algorithms in HTR simulator TINTE, 2018 [3] Coupled Newton–Krylov time-spectral solver for flutter and limit cycle oscillation prediction, 2021
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript presents the development of an implicit discontinuous Galerkin solver for turbulent real gas. There are in my view a number of technical and editorial inadequacies, in the manuscript, which need to be revised as well as revisited.
Major comments:
- The manuscript is in the stage of a draft and requires major revisions to meet the standards of Fluids journal.
- The results section is very brief and thus, the manuscript lacks important analysis and data. The authors should perform a more in-depth analysis.
- Although the authors present some of the qualitative CFD results, there is a significant amount of quantitative data, which can be collected from the CFD analysis. Therefore, the authors should present more quantitative data obtained from the CFD analysis.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
No further comments
Reviewer 2 Report
More qualitative and quantitative results would enhance the technical content of the paper.
