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I am trying to better understand the FAS multigrid algorithm for Euler equation in FV discretization. The usage of the modified residual (the residual with forcing) inside the different cases:

  • Unsteady computations : referring to the Jameson's paper I understand that it is used in the dual time step computation that allows for a faster convergence. This fact seems confirmed by this paper, where a similar approach is used.
  • Steady computations: if I have well understood (seen that there is not the time integration) is used in the linear solver process, hence for example with a Krylov based method.

I wanted to ask if these two points are correct, and, in the second case, if we have to rely compulsorily on a Krylov based method (e.g GMRES). From my understanding another solver (e.g Jacobi) would not take into account the modified residual with forcing and so would not take into account the history of the different multigrid levels residual, making the multigrid algorithm ineffective.

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