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## Convergence Monitoring

Monitoring and properly assessing convergence levels during a Wind-US run are critical in obtaining meaningful, useful results. Wind-US allows you to track convergence by following residuals and/or integrated forces, moments, and mass flow. For engineering applications, the recommended convergence monitoring method is the tracking of integrated quantities of interest. For example, if you are modeling a wing/body geometry to determine drag, you should monitor integrated drag and set some reasonable bounds on drag oscillations as your convergence criterion.

### Residuals

In steady-state (non-time-accurate) solutions, the residuals are the amounts by which the solution vector changes in a single iteration. Ideally, in approaching a steady state solution, the residuals should approach zero. However, in practice, complex geometric and flowfield features may limit the reduction in the residuals to about two orders of magnitude. Wind-US prints solution residuals to the list output file, in order to get a general idea of solution convergence.

For structured grids, Wind-US organizes the equations to be solved into logical "groups" that are solved together. For example, when a one- or two-equation turbulence model is used, the Navier-Stokes equations and the turbulence model equations are in two separate groups.

For each equation group in each zone, Wind-US prints the zone number, cycle number, location of the maximum residual (i, j, and k indices), equation number for which the maximum residual occurred, the value of the maximum residual, and the L2-norm of all the residuals for all the equations over all the points in that zone. The L2-norm of the residuals will give you an idea of the overall convergence of the solution. The location of the maximum residual may give you insight into problems with a particular solution. After solution "bombs" or when convergence is unacceptably slow, the location of the maximum residual is the first place you should look for potential problems with the solution.

The residuals are printed by default each iteration. The output interval may be changed, however, using the CYCLES and ITERATIONS keywords. Residuals may also be plotted by first using the auxiliary program resplt to generate a GENPLOT file, then using that file as input to the plot command in the CFPOST post-processing package.

By default, if the maximum residual for an equation group decreases by four orders of magnitude in a particular zone, a "converged" message is printed in the list output file, and iterations for that group in that zone are ended for the current cycle. Note that, if the residuals early in the calculation are large due to large initial solution transients, Wind-US may decide that a zone is converged when it may require significantly more iterations. In the input data file, with the CONVERGE keyword you can specify different convergence criteria, by setting the amount the residual must decrease, and by telling Wind-US to use the value of the residual rather than an order-of-magnitude reduction. You can also specify use of the L2-norm of the residual instead of the maximum residual using TEST option 128.

Keywords: CONVERGE, CYCLES, ITERATIONS, TEST 128

### Integrated Flowfield Quantities

As noted above, the optimal convergence checking criterion for a solution is an integrated quantity of interest for a particular study. For example, for an afterbody drag study to calculate pressure drag, the integrated drag is obviously the best quantity to track in monitoring convergence. This may be accomplished using Wind-US's flowfield integration capability. In the input data file, you may specify a number of computational surfaces for which Wind-US will integrate forces, moments, and/or mass flows. If you specify reference length, area, and moment center, Wind-US will output the forces and moments as coefficients; you may even specify output of lift and drag coefficients in place of x and y force coefficients.

You may specify zones and computational grid indices of subsets to be integrated, and you may request that different quantities be integrated on each subset. You may also control the frequency of output and whether the code outputs subset totals and/or zonal and grand totals. The auxiliary program resplt will produce GENPLOT plot files of output integration quantities versus solution cycle number, which may then be used as input to the plot command in the CFPOST post-processing package.