When solving for a Navier-Stokes model using an unsteady algorithm, does the grid refinement guarantee convergence to the experiment?

While refining the grid can often improve the accuracy of computational fluid dynamics (CFD) simulations, the convergence of the solution to the experimental result is not guaranteed. This is because convergence is contingent on many factors beyond just grid refinement. Even with a consistent and stable model and appropriate boundary conditions, discrepancies between the model and the actual physics, limitations in the numerical methods used, round-off and truncation errors, and various subgrid-scale phenomena that may not be fully resolved or properly modeled can all influence the final results and potentially prevent them from converging to experimental results. Moreover, even if one were to infinitely refine the grid, there would be physical phenomena that the Navier-Stokes equations, especially the unsteady ones, simply cannot capture. These are the so-called turbulence scales that must be considered when comparing with experimental results. Therefore, additional turbulence models might be necessary to accurately simulate these more complex systems. Furthermore, experimental errors, uncertainties in the boundary and initial conditions, as well as the simple fact that real-world flows are often three-dimensional and unsteady while the CFD model might not be, would all prevent a guaranteed convergence. In summary, although refining the grid might improve the simulation results, a full convergence between the experiments and the simulations would not be guaranteed. Further validation and verification, model refinement, and potentially more sophisticated numerical techniques would be needed to increase confidence in the model results or achieve a better match with experimental results.

No, its solution's convergence to the experiment is not guaranteed when the grid is refined. The accuracy of the solution of the unsteady Navier-Stokes model is dependent on several factors, such as the number of iterations, grid size, the choice of numerical scheme and the boundary conditions, among other factors. Thus, although the model is consistent and stable, its solution may not converge to the experiment when the grid is refined.