Perform Fluid Flow Analyses

Segregated Formulations

With the segregated formulation, there are potentially two sets of iterations. One set of iterations |R/F| = relates to the solution of the velocity and pressure matrices when using the iterative solver. The other set of iterations relates to the convergence of the fluid flow equations. After the velocity and pressure matrices converge with the iterative solver, the error norm in the fluid flow equations are calculated.

Using the segregated formulation, the columns in convergence history are as follows (see Figure 1):

• Step Intv: the time step interval corresponds to the input between two rows of the load curve spreadsheet (or between the initial value and the first row in the case of steady fluid flow).
• Step: the step number within the step interval, from 1 to the number of Steps entered in the load curve.
• Time: the time corresponding to the time step.
• Percent: the percent of the analysis that is completed once the current time step converges.
• DT: the current time step size.
• L: the time step level. The analysis begins at level L=1. Unlike the other formulations, the segregated formulation will not increase the time step level (no time step reductions).
• NonL Iter: the iteration number for the current time step (the iteration to solve the fluid equations). If the iteration reaches the Max Iterations specified under the load curve, then twice as many iterations will be added to the iterations already completed. The letter i will be placed next to the iteration number to indicate that iterations are being added. This can be repeated 5 times for unsteady flow (6 times for steady flow), each time adding twice as many iterations as before (except for the last increase). So if the Max Iterations was set to 5, the total number of iterations that could be performed with this scheme is 5+10+20+40+80+80 = 235 iterations.
• Solv. Iter: This column indicates how many iterations were required for the solution of the velocity and pressure matrices when using the iterative solver. If using the sparse solver, these lines will not appear in the output. Multiple lines of output may appear with a different Solv. Iter number shown. Due to the solution method, the velocity in three directions and the pressure each must converge and can converge with a different number of iterations. These are shown as |R/F|u =, |R/F|v =, |R/F|w =, and |R/F|p =, respectively, when using the iterative solver. A c at the end of these lines indicates that the solver iteration has converged for the respective item and the residual is smaller than the Convergence tolerance value specified on the Solution tab of the Analysis Parameters.
  TipIf the pressure |R/F|p is requiring many iterations to converge, or reaches the maximum number of iterations before converging, consider changing the pressure solver from iterative to a sparse solver. When the maximum number of iterations have been used, the letter m will appear at the end of the line.
• R_Norm_V or A_Norm_V: Once the solver iterations converge, the fluid equation norm is given (the number in this column of the output). The _Norm_V is the Euclid L-2 norm between two iterations based on the velocity. The R at the beginning of the title indicates the relative norm is used, and A at the beginning of the title indicates the absolute norm is used. If the norm is smaller than the Velocity Norm specified, then the velocity solution has converged. (All convergence parameters are specified on the Load Curves tab of the Analysis Parameters screen.)
• R_Norm_P or A_Norm_P: Once the solver iterations converge, the fluid equation norm is given (the number in this column of the output). The _Norm_P is the Euclid L-2 norm between two iterations based on the pressure. The R at the beginning of the title indicates the relative norm is used, and A at the beginning of the title indicates the absolute norm is used. If the norm is smaller than the Pressure Norm specified, then the pressure solution has converged. (All convergence parameters are specified on the Load Curves tab of the Analysis Parameters screen.)

• c: When the nonlinear iteration converges, the letter c appears after the _Norm_V or _Norm_P values. Both the velocity and pressure norms must be smaller than the respective tolerance in order for the fluid equations to be converged, at which time the solution proceeds to the next time step.
• s: When the fluid timestep is oscillating due to stagnation, the letter s appears after the _Norm_V or _Norm_P values. What happens in this situation depends on the setting chosen for the Detect stagnation due to oscillation pull-down.

With the previous explanation in mind, the sample log file can be interpreted as follows:

• At time step 1, nonlinear iteration 1 (fluid equations), the iterative solver required 1 iteration to converge on the v component of the velocity (line 04) and 8 iterations to converge on the pressure (line 05). The norms for the nonlinear velocity and pressure were both 1.000E+00 (line 06).
• For nonlinear iteration 6, the iterative solver again required only 1 iteration to converge on the u, v, and w components of the velocity matrices (lines 27, 28, 29) and 8 iterations for the pressure matrix (line 30). The velocity norm 9.295E-03 was smaller than the convergence tolerance and therefore converged (line 31), but the pressure norm 1.552E-02 was larger than the tolerance; thus, the time step has not converged. The solution continues to the next iteration.
• On nonlinear iteration 7, both the velocity and pressure norms are smaller than the convergence tolerances (note the c after each value), so the time step has converged (line 36). The next output line (not shown in the figure) would be for the next time step.

Other Formulations:

Using the Penalty formulation or Mixed GLS formulation, the columns in convergence history are as follows (see Figure 2):

• Step Intv: the time step interval corresponds to the input between two rows of the load curve spreadsheet (or between the initial value and the first row in the case of steady fluid flow).
• Step: the step number within the step interval, from 1 to the number of Steps entered in the load curve.
• Time: the time corresponding to the time step.
• Percent: the percent of the analysis that is completed once the current time step converges.
• DT: the current time step size. If the analysis is having difficulty converging, it may reduce the time step by half.
• L: the time step level. The analysis begins at level L=1. When L increases by one, the time step is cut in half.
• NonL Iter: the iteration number for the current time step. If the iteration reaches the Max Iterations specified under the load curve, then one of two possibilities will be used:
  1. If the residuals from the last three iterations are increasing, the time step level L will be increased and the time step will be cut in half. This can continue up to level 20 at which point the processor quits.
  2. If the residuals from the last three iterations are decreasing, twice as many iterations will be added to the iterations already completed. The letter i will be placed next to the time step level L to indicate that iterations are being added. This can be repeated 5 times, each time adding twice as many iterations as the Max Iterations as before. So if the Max Iterations was set to 5, the total number of iterations that could be performed with this scheme is 5+10+20+40+80+160 = 315 iterations.
• Residual Norm: The residual norm between two iterations based on the Navier-Stokes equations. If (R) appears in the title, then the relative norm is used; otherwise, an absolute norm is used. If the residual norm is smaller than the Residual Tol specified on the load curve, then the time step has converged.
• Increm. Norm: The error norm between two iterations based on the velocity. If (R) appears in the title, then the relative norm is used; otherwise, an absolute norm is used. When the increment norm is smaller than the Increment Tol specified on the load curve, then the time step has converged.
• c: When the timestep converges, the letter c appears at the end of the line.
  NoteEither the residual tolerance or the increment tolerance must be satisfied to converge. Both tolerances do not need to be satisfied. The convergence is often satisfied by the residual tolerance even though the increment norm can still be somewhat large. A large increment norm indicates that the velocity change between iterations is large. Therefore, check the log file after the analysis completes to make sure your requirements are satisfied.

With the above explanation in mind, the sample log file can be interpreted as follows:

• In time interval 1 (lines 04 through 09), both time steps were able to converge after 3 iterations (lines 06 and 09).
• In time interval 2 (lines 12 through 19), both time steps were able to converge after 4 iterations (lines 15 and 19).
• Both the residual norm and increment norm are small. In particular, a change in velocity of 4.477E-7 and 2.932E-6 (the increment norms) are much smaller than the magnitude of the velocities. Thus, the solution is well converged.