[Murielle MG]

Dear Foamers,

I am seeking your guidance and assistance in the implementation of JFNK (Jacobian-Free Newton-Krylov) methods based on the Gmres solver in foam-extend-4.1 for my current project.

To provide some context, I am working on an open-source software based on Foam Extend. In order to enhance the accuracy and efficiency of simulations, the JFNK method has been identified as a potential solution to achieve these objectives.

However, my limited familiarity with OpenFOAM, Foam Extend, and C++ is posing challenges in effectively implementing this method. Therefore, I kindly request your help on the following aspects:

1. How to modify the existing Foam Extend (GMRES) codebase to effectively incorporate the JFNK method.

For this first point, I have made a copy of the GMRES solver files within a "libraries" folder in my application in order to make changes to the GMRES solver as it seems difficult to built a general Gmres JFNK solver.
In the existing code (BlockGMRES and gmresSolver files), what I identified in the existing code (present in the BlockGMRES and gmresSolver files) is that the matrix.Amul command should be replaced by the finite difference of the numericals fluxes for the JFNK method as shown in the file attached. The numerical flux phi (u^k) refers to argument b of the GMRES method.
My difficulty lies therefore in constructing the second numerical flux phi (u^k+epsilon*z) as it is expected to change in every iteration.

I therefore tried to obtain in this solver the variables allowing the construction of the numerical flux such as: rho, rhoU, rhoE (to built it directly in the solver) by using the following command :

const volScalarField& rho = this->Mesh_.lookupObject<volScalarField>("rho");

but this command doesn't work.

The first error is :

error: 'class Foam::BlockGMRES<Foam::Tensor<double> >' has no member named 'Mesh_'

Which brings me to the second point.

2. How to obtain from this solver, the values of the variables present on the mesh. (If I am on the right path to mplement the JFNK in the GMRES solver)

I sincerely appreciate any support or guidance you can provide regarding these challenges.

Thank you in advance for your assistance.