[Torque_Converter]

I have seen in many codes documentation that the orders of magnitude of residual drop depends on how close the initial condition is to the final answer. A 5 order of magnitude drop may not even be possible if the initial guess is practically at the solution somehow.

However, CFX documentation says that due to their residual normalization scheme the residual drop is initial guess independent. That seems to indicate that no matter how good your initial guess is you should expect the same order of magnitude drop. Is this true/possible? Is this due to normalization based on the initial guess values somehow so that even if u-momentum only needs to change by 0.00001 kg*m/s because of a good initial guess it will still show it has dropped by 5+ orders of magnitude when finally converged (quickly converged I imagine being that close to the final answer).

[Opaque]

Residuals drop does not say anything about convergence besides that the iterations are going in the right direction, i.e. it is not diverging.

For example, if you start from the exact solution, the residual drop would be 0 (or undefined) since the residual is already 0.

[Torque_Converter]

Yes, I understand the definition and function of residuals academically as well as professionally. Documentation on other codes I have worked with (Numeca, Star-CCM+) make it clear that the residuals are initial guess sensitive. This only makes sense. How can an answer change by much if it is already incredibly close to the starting point?

However, CFX documentation states that the "residuals are initial guess independent". That would lead me to believe somehow, via some normalization, that no matter how close your initial is to the answer it will expect a big residual drop. Perhaps through division of the values by the initial, resulting in an artificially big number? I don't know, they don't detail all of their normalization methods, simply have that odd statement.

I am curious to know because many solutions drop to deep residual levels (below 1e-6 RMS) while some others, which have acceptable monitor point convergence only drop to 1e-4 RMS. I know the monitor points, and often imbalances are more important, however, it is something that confuses me about residuals in CFX.

[Opaque]

The residual normalization procedure is explained in the ANSYS CFX documentation

Chapter 11: Discretization and Solution Theory | 11.2. Solution Strategy - The Coupled Solver

11.2.3. Residual Normalization Procedure

As described above, the raw residual, [r], is calculated as the imbalance in the linearized system of discrete equations. The raw residuals are then normalized for the purpose of solution monitoring and to obtain a convergence criteria. An overview of the normalization procedure is given below.

For each solution variable, , the normalized residual is given in general by:


(11–53)

where is the raw residual control volume imbalance, ap is representative of the control volume coefficient, and is a representative range of the variable in the domain. The exact calculation of ap and is not simple and is not presented here. However, some important notes are:

The normalized residuals are independent of the initial guess.

ap is the central coefficient of the discretized control volume equation and therefore includes relevant advection, diffusion, source linearization, and other terms.

For steady-state simulations, the time step is used only to underrelax the equations and is therefore excluded from the normalization procedure. This ensures that the normalized residuals are independent of the time step. The transient term is included in ap for transient simulations.

For multiphase, if equations are coupled through an interphase transfer process (such as interphase drag or heat transfer), the residuals are normalized by the bulk ap.

Unfortunately, the equation did not cut/paste properly.. But, you should be able to find it in the proper section..

Hope the above helps,

[Torque_Converter]

That is the section I found as well. What I meant by not being fully explained is that while you learn the basic normalization procedure (which makes sense) you do not learn what the cell coefficient happens to be, for example.

But more importantly is the line "The normalized residuals are independent of the initial guess."

I may be missing something, I admit, but the other codes I have worked with said normalization was dependent on initial guess, meaning if the initial guess is good the residuals may not change much, so the best way to judge convergence is via monitor points of critical characteristics. Here appears to say the opposite, and via some proprietary item in the normalization variables the residuals should drop to some absolute point to be considered converged. I.e. 1e-5 or so.

[ghorrocks]

Yes, the exact details of the residuals calculation are propriety and are not disclosed (unfortunately). A better way of looking at the residuals is that for most steady state simulations residuals = 1e-4 means approximate convergence, 1e-5 means convergence good enough for most design purposes and 1e-6 means very tight convergence. This is what it means initial conditions independence (and independence from just about everything else too, actually).