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Improving Simulation Times Using the Implicit Advection Model

This article was contributed by David Souders, VP of Sales, Marketing and Customer Support.


Threshhold Option Window in FLOW-3D

FLOW-3D’s locally-implicit advection solver has been enhanced to enable the user to directly control the level of explicit and implicit approximations of advective momentum fluxes within the solution domain. This additional functionality is designed to further improve simulation completion times by maintaining a larger time step than a fully explicit method yet still small enough to resolve essential flow features. Typically an explicit solution is considered to be more accurate and slower to complete due to strict time-step limitations. Implicit methods can take much larger time steps but tend to lose accuracy or create a more diffuse solution.

This locally-implicit method is powerful in its selectiveness and flexibility but should be tested for any particular simulation type it is applied to in order to create the best balance between accuracy and speed improvement. As shown in Figure 1, this new option includes a threshold velocity or a target time step.

The objective of this article is to test the threshold options model for achievable speed improvement and determine at what point accuracy starts to become lost. Figure 1 shows where to locate the model and the settings available. There are two modes: Velocity Threshold and Target Time Step. These modes will be tested for a high pressure die casting (HPDC) case and a hydraulics spillway case.


Metal Casting Test Simulation

This test case is the fast shot of a high pressure die casting. Four simulations were run for comparison. The semi-implicit option means completely filled cells are treated implicitly and free-surface cells explicitly. Other than running fully explicit, this is considered the most accurate solution possible for the variations tested. It will be the benchmark standard against which the threshold options variations will be compared for this article. The average time step for this case was 2.0e-6 s.

Benchmark Simulation — Locally Implicit Advection

Benchmark Casting Simulation

In Figure 2B the final location of surface oxides at the end of fill are trapped in the part in the problem areas. This is another measure of the likelihood of defect problems in the same location as that of the experimental data.

This simulation is a validation case that matched the experiment making it an excellent test case. It was found that porosity existed in the base and the chimney due to the way the molten metal filled the casting. The metal would back fill making the last regions close the cavity contain the earliest metal that entered. This means air pockets formed where there was early solidification. The highest concentrations of surface oxides were also located within the part in that same location and high concentrations are found throughout much of the chimney where porosity problems also existed.

Variation 1 — Velocity Threshold Set at Gate Velocity

For this variation the gate velocity (18.8 m/s) was chosen as the velocity threshold based on the assumption that any velocities exceeding the gate velocity are spurious droplets and negligible. The average time step was 3.0e-6 s, so a little higher than the previous case. Speed up was 1.18 times faster. A slight difference in the void closure can be seen at about t = 2.83e-3 s. At the end of fill there is roughly the same result in terms of surface defect concentration but perhaps a little more diffusion in the result. The overall flow pattern and final defect locations tend to match well.

Variation 1 — Velocity Threshold Set at Gate Velocity

Variation 2 — Time Step Set to Double the Average Time Step for Threshold Velocity

The time step was set to double that of average time step for gate velocity threshold to see what sort of improvement might be found. The speed up over the benchmark was 1.95 times. The time step averaged to 5.55e-6 s. This is a significant improvement in completion time as it is essentially half. The results again have a slight variation but still show roughly the right filling pattern and final defect locations.

Variation 2 — Time Step Double Average Time Step for Threshold Velocity

Variation 3 — Time Step Set to 1.0 s

The final test was to set the time step at a very high value of 1.0 second to determine how fast the simulation can complete. What occurred was that the next stability criterion, a viscous time-step limit, took precedence and held down the time step below the value of 1.0 s. The average value was only 2.24 times that of variation 2. In this final test the speed up over the benchmark was 2.17 times. The results on the other hand are the most significantly varied. During the fill the pattern is showing a more slug-like flow with the void not closing up as quickly and the fluid back-filling down the chimney is also more slug-like than the jets of fluid found previously.

Variation 3 — Time Step Set at 1.0

The oxide concentrations at the end of fill are in roughly the same locations, however, there are much sharper contrasts throughout the distribution.

Comparison Table

Shown here is an overall review of the benchmark and the three variations. Volume error can be considered a strong indicator of numerical error in a simulation in some cases. Note that the volume error in the final variation is 10% while the other simulations are at a fraction of a percent.

Table 1 – Data chart on casting variations.
Numerical Details Average Time Step Time Speed Up Volume Error
Semi implicit (default) 2.000E-06 s 0.124 hours 1.00 0.50%
Target (gate) velocity of 18.8 m/s 3.000E-06 s 0.105 hours 1.18 0.50%
Target time step of 6e-6 s 5.551E-06 s 0.066 hours 1.88 0.75%
Target time step of 1 s 1.243E-05 s 0.057 hours 2.17 10%

Water & Environmental

With many hydraulics simulations the goal is a quasi-steady state result so the transient to get to this condition will not be evaluated. What will be measured is the overall free-surface elevation to be sure surface waves and hydraulic jump details are not being lost and the overall flow velocities and patterns will be checked to find out whether there are significant deviations in the flow currents. A hydraulics simulation is considered to be at steady state when the overall kinetic energy and turbulent energy become constant. All results shown are compared at these conditions.

Benchmark Simulation — Locally Implicit Advection

Benchmark Simulation — Locally Implicit Advection

The benchmark for comparison is the same setting as the high pressure die casting in that the locally-implicit model is run with no further adjustments. The average time step achieved is 2.0e-6 s. Shown in Figures 6a and 6b are velocity magnitude profiles and free-surface elevation for comparison as possible speed up is evaluated in the subsequent variations. Two velocity threshold values and one time step setting were tested. The maximum velocity on the spillways is about 22 m/s. Velocity thresholds of 12.0 and 2.5 m/s were randomly chosen for comparison. Also selected was a time-step threshold with a value of twice the average time step achieved when running the implicit velocity threshold of 2.5 m/s.

Variation 1 — Velocity Threshold of 12.0 m/s

Variation 1 — Velocity Threshold of 12.0 m/s

The first variation used a velocity threshold of around ½ that of the maximum velocity reached on the spillway. This value was chosen randomly. The speed up was 1.66 times that of the benchmark. Both visually and numerically the results do not deviate much from the benchmark case meaning it is a reasonable set of results based on velocity and surface profiles.

Variation 2 — Velocity Threshold of 2.5 m/s

Variation 2 — Velocity Threshold of 2.5 m/s

Because variation 1 worked well, a more extreme test with a cutoff threshold of 2.5 m/s was chosen for variation 2. Again the results compare well with a slightly more significant variation in the flow pattern. The gain in completion time for this case was 3.06 times that of the benchmark case.

Variation 3 — Time Step Set to 0.026 s

Variation 3 — Time Step Set at 0.026

For this case a time step of about double the average time step of variation 2 was chosen. The speed up was incredible in that it was over 45 times faster to complete than the benchmark case. However, this simulation lost a lot of detail in the flow pattern and, as in the final casting case, the fluid has a more slug-like appearance to it. The volume error remained minimal in this case regardless of the loss in accuracy meaning it is not a good measure of accuracy in every simulation.

Comparison Table

Shown here is an overall review of the benchmark and the three variations.

Table 2- Data chart on water and environmental variations
Numerical Details Average Time Step Time Speed Up Volume Error
Semi implicit (default) 4.044E-03 s 5.553 hours 1.00 -0.01%
Target velocity of 12.0 m/s 3.056E-03 s 3.338 hours 1.66 -0.01%
Target velocity of 2.5 m/s 1.330E-02 s 1.817 hours 3.06 -0.05%
Target time step of 0.026 s 2.574E-02 s 0.121 hours 45.74 0.02%


It has been shown that significant speed improvement can be achieved using velocity or time-step controls on the locally-implicit advection model. However, attention to accuracy must always be considered. One school of thought could be to use the model for quickly testing design variations with a reasonable allowable error and once a good design is honed in on, a final simulation can be run fully explicit or locally-implicit with no threshold set for confidence in the final result.

It is also important to note that other factors can cause the time step to drop. When running a simulation, depending on the physical models selected, there can be other stability criteria which become the limiting factor. If this is the case then the time step will not go beyond that limit. For example, if viscosity is the limiter then the time step will be controlled by it. Another contributor to a time-step reduction can be excessive iterations. If FLOW-3D has a high iteration count for convergence then the time step will be reduced to help achieve convergence. During the testing of the model it was also found that pushing the time-step threshold can cause a lack of convergence.

In the future, FLOW-3D may be able to make informed decisions on how much a simulation can be accelerated and maintain a measureable degree of accuracy. Until then, it is important to make informed decisions through testing when applying this feature. In these variations it has been demonstrated that speed improvements of 1.2 to 3.0 times can be achieved and maintain a reasonable degree of accuracy. A three day simulation might now be completed in one day without requiring an investment in hardware improvement.

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