Convergence Plot

After the analysis is finished, display the convergence information by clicking the Convergence Plot tab on the Output Bar.

The primary criteria for determining convergence is that the change of each degree of freedom is minimized over a large range of iterations. The curves shown in the Convergence Monitor are plots of the average value of each degree of freedom throughout the entire calculation domain.

To learn more about Automatic Convergence assessment

Degrees of Freedom

A useful way to look at convergence data is to examine each degree of freedom individually. Select one from the Quantity drop menu (the default value is All). The maximum and minimum values of the quantity are shown on the Y-axis of the plot.

For more information about TKE and TED

Iteration Range

Adjust the displayed range of iterations by changing the Start and/or End iteration values. Implement the change by clicking Enter on your keyboard. This is especially helpful for hiding the first 50 iterations from the convergence plot. Before iteration 50, the quantities are typically changing too much to be considered when assessing convergence.

By default, the average value of each degree of freedom is plotted. To view the maximum and minimum values, select Min. or Max. from the menu at the right side of the dialog.

Click the Table tab to view the values in the plot. Show values for a single degree of freedom by selecting it from the menu on the right.

Plot Quantities and Error Estimation

Several parameters can be plotted with the Convergence Monitor to aid in understanding analysis progress:

These quantities are used by Intelligent Solution Control and Automatic Convergence Assessment to ensure the stability and convergence of the analysis.

Select them from the second pull-down menu on the right side of the Convergence Monitor (the default value is All). Each quantity is described briefly:

• Avg: The average value of the plotted quantities.
• Min: The minimum value of each quantity over the displayed range of iterations.
• Max: The maximum value of each quantity over the displayed range of iterations.
• Resid In: This is the residual value of each degree of freedom, and is the measure of how much the quantity is changing. This is the residual quantity that was plotted in previous versions of Autodesk Simulation CFD.
• Resid Out: This value should be quite small, and is the value of the residual over the entire field after the last iteration.
• Solv Iter: The number of sweeps per iteration required by the solver for each degree of freedom.
• Relax Parm: The under-relaxation value invoked by the Intelligent Solution Control for each quantity. If Intelligent Solution Control is not enabled, then these are the values specified on the Convergence Controls dialog.
• DPhi/Phi: The fluctuation value of each field variable. This is used by Intelligent Solution Control and Auto Stop to assess the analysis rate of change.

More about Resid In and Resid Out

The residuals that are displayed during an analysis can be thought of as a measure of how well a solution vector X satisfies a matrix equation.

The objective is to solve a matrix equation: AX = b.

The residual vector, r is defined as, r = b - Ax.

The L2 norm is typically used as it is a single value that characterizes the solution rather than a residual vector:

L2_norm ( r ) = sqrt (sum of the squares of the individual r vector terms)

For example, if the residual value is 1.05E+2, the solution may not be bad since we are:

• commuting a residual vector ( number of terms = number of nodes ),
• squaring all the individual terms,
• summing it all up and finally taking the square root.

So for a 1 million node model, with an L2 residual = 1.05E+02, the average error at a node = 0.105. If this is for temperature, then there is on average a 0.105 K error in terms of how well the temperature solution satisfies the energy equation.

The difference between Residual In and Residual Out:

Resid In = L2_norm ( AX - b ) before the solver converges.

The Autodesk Simulation CFDSolver forms A and b using the energy equation and uses the last value of X ( temperature ) to compute the L2_norm ( AX - b ).

Resid Out = L2_norm ( AX - b ) after the solver has converged. The Solver outputs a solution vector X ( temperature ) and uses this to compute the residual going out of the solver.

For a convergence criteria = 1.0E-08:

Resid Out = 1.0E-08 * Resid In

This specifyies that you the out-going residual is to be 8 orders of magnitude smaller than the incoming residual.

For pressure and temperature, the outgoing residual, Resid Out should be much smaller than the incoming residual, Resid In.