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Tips & Tricks: Convergence and Mesh Independence Study
Jan17

Tips & Tricks: Convergence and Mesh Independence Study

The previous posts have discussed the meshing requirements that we need to pay attention to for a valid result. It is important to remember that your solution is the numerical solution to the problem that you posed by defining your mesh and boundary conditions. The more accurate your mesh and boundary conditions, the more accurate your "converged" solution will be.   CONVERGENCE Convergence is something that all CFD Engineers talk about, but we must remember that the way we generally define convergence (by looking at Residual values) is only a small part of ensuring that we have a valid solution. For a Steady State simulation we need to ensure that the solution satisfies the following three conditions:   - Residual RMS Error values have reduced to an acceptable value (typically 10-4 or 10-5) - Monitor points for our values of interest have reached a steady solution - The domain has imbalances of less than 1%.   RMS Residual Error Values   Our values of interest are essentially the main outputs from our simulation, so pressure drop, forces, mass flow etc. We need to make sure that these have converged to a steady value otherwise if we let the simulation run for an additional 50 iterations then you would have a different result. Ensuring that these values have reached a steady solution means that you are basing your decisions on a single repeatable value.   Example of Monitoring a Value of Interest   As a rule, we must ensure that prior to starting a simulation we clearly define what our values of interest are, and we make sure that we monitor these to ensure that they reach a steady state. As previously highlighted, we also need to make sure that the Residual RMS Error values are to at least 10-4. Finally, we need to ensure that the overall imbalance in the domain is less than 1% for all variables.   Imbalances in the Domain     MESH INDEPENDENCE STUDY The approach outlined above results in a single solution for the given mesh that we have used. Although we are happy that this has "converged" based on RMS Error values, monitor points and imbalances, we need to make sure that the solution is also independent of the mesh resolution. Not checking this is a common cause of erroneous results in CFD, and this process should at least be carried out once for each type of problem that you deal with so that the next time a similar problem arises, you can apply the same mesh sizing. In this way you will have more confidence in your results.   The way we...

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