RECOMMENDATIONS ON GRIDS

The key recommendation is to ensure smooth grids, avoiding abrupt changes in grid size or shape, as this can lead to a significant loss of accuracy. Hence take good care to:

? Define the computational domain, in order to minimize the influence and interactions between the flow and the far-field conditions. In particular,

– Place inlet and outlet boundaries as far away as possible from the region of interest. In particular, if uniform far-field conditions are imposed, you should ensure that the boundary is not in a region where the flow may still vary significantly.

– Avoid inlet or outlet boundaries in regions of strong geometrical changes or in regions of recirculation.

? Avoid jumps in grid density or in grid size.

? Avoid highly distorted cells or small grid angles.

? Ensure that the grid stretching is continuous.

? Avoid unstructured tetrahedral meshes in boundary layer regions.

? Refine the grids in regions with high gradients, such as boundary layers, leading edges of airfoils and any region where large changes in flow properties might occur.

? Make sure that the number of points in the boundary layers is sufficient for the expected accuracy. Avoid less than 10 points over the inner part of the boundary layer thickness.

? Monitor the grid quality by adequate mesh parameters, available in most of the grid generators, such as aspect ratio, internal angle, concavity, skewness, negative volume.

RECOMMENDATIONS ON SOLUTION ASSESSMENT

Once you run your code, the following recommendations will be useful to enhance your confidence in the results obtained:

? Check very carefully the selected boundary conditions for correctness and compatibility with the physics of the flow you are modeling.

? Verify all the numerical settings and parameters, before launching the CFD run.

? Verify that your initial solution is acceptable for the problem to be solved.

? Monitor the convergence to ensure that you reach machine accuracy. It is recommended to monitor, in addition to the residuals, the convergence of representative quantities of your problem, such as a drag force or coefficient, a velocity, temperature or pressure at selected points in the flow domain.

? Look carefully at the behavior of the residual convergence curve in function of number of iterations. If the behavior is oscillatory, or if the residual does not converge to machine accuracy by showing a limit cycle at a certain level of residual reduction, it tells you that some inaccuracy affects your solution process.

? Apply internal consistency and accuracy criteria, by verifying:

– Conservation of global quantities such as total enthalpy and mass flow in steady flow calculations.

– The entropy production and drag coefficients with inviscid flows, which are strong indicators of the influence of numerical dissipation, as they should be zero.

? Check, whenever possible, the grid dependence of the solution by comparing the results obtained on different grid sizes.

? Some quantities are more sensitive than others to error sources. Pressure curves are less sensitive than shear stresses, which in turn are less sensitive than temperature gradients or heat fluxes, which require finer grids for a given accuracy level.

? If your calculation appears difficult to converge, you can

– Look at the residual distribution and associated flow field for possible hints, e.g. regions with large residuals or unrealistic levels of the relevant flow parameters.

– Reduce the values of parameters controlling convergence, such as the CFL number or some under-relaxation parameter, when available.

– Consider the effects of different initial flow conditions.

– Check the effect of the grid quality on the convergence rate.

– Use a more robust numerical scheme, such as a first order scheme, during the initial steps of the convergence and switch to more accurate numerical schemes as the convergence improves.

RECOMMENDATIONS ON EVALUATION OF UNCERTAINTIES

? This is a very difficult issue, as the application uncertainties are generally not well defined and require a sound judgment about the physics of the considered flow problem. Some recommendations can be offered:

? Attempt to list the most important uncertainties, such as

– Geometrical simplifications and manufacturing tolerances around the CAD definition.

– Operational conditions, such as inlet velocity or inlet flow angle.

– Physical approximations, such as handling an incompressible flow as a low Mach number compressible flow. This type of uncertainty is manageable, as it can more easily be quantified.

– Uncertainties related to turbulence or other physical models.

? Perform a sensitivity analysis of the relevant uncertainty to investigate its influence.