Top > Resource Library > Master Course for Fluid Simulation Analysis of Multi-phase Flows by Oka-san > No.5
This chapter discusses calculation time, which is an important consideration when free surface problems are solved using the VOF method.
Since free surface flow analyses using the VOF method are transient analyses, they require more calculation time than steady-state analyses. If the calculation is unstable, the time step (or Courant number) must be reduced. To prevent interface diffusion caused by numerical calculation error, the mesh near the interface must have fine resolution. The calculation time will increase for both of these cases.
Different methods can be used to reduce the calculation time. One of the methods will be introduced by showing an analysis example.
In this example, oil sloshing in an oil tank due to an earthquake will be analyzed. As shown in Figure 1, the oil tank is 42.7 m in diameter and 24.4 m high. Its maximum capacity is 30,000 kL of oil. In this example, 26,000 kL of oil (density: 740 kg/m^{3}
, viscosity: 0.0026 Pa∙s, surface tension coefficient: 0.020 N/m) is stored. The oil level height is 18.2 m. The tank shakes laterally with a lateral acceleration of 1 m/s^{2}
for 10 seconds. The movement is caused by a long-period earthquake ground motion with a period of 5 seconds. A structural mesh with 1,306,800 uniform elements is used for the inside of the tank, and the analysis is performed using the MARS (Multi-interface Advection and Reconstruction Solver) method for 60 seconds in real time. The time step is automatically set so the Courant number will not exceed 0.9.
Figure 2 shows the analysis result, for the behavior of the oil surface. When the background is blue, the tank is shaking for 10 seconds. When the background is white, the tank remains stationary for 50 seconds. Figure 2 shows that the oil surface reaches the highest position several seconds after the earthquake stops. The oil surface gradually lowers; however, sloshing continues even after 60 seconds. The analysis calculation time to produce these results is approximately 4 hours. Actual time will depend on the program code and the computers used.
What can be done to reduce the calculation time? Since the earthquake motion is laterally unidirectional, a symmetry plane can be defined as shown in Figure 3. When the symmetry plane is used, the number of elements can be reduced in half and the calculation time by over 50%.
Another way to reduce the calculation time is to take advantage of parallel processing. In this example, the program code can be parallelized by MPI (Message-Passing Interface) or another method in combination with the hardware computing platform using a multi-core CPU. Parallel computing has the potential to reduce the current calculation time by 47%.
To further reduce calculation time, a coarser mesh can be used without decreasing the calculation accuracy. As shown in Figure 4, a coarser mesh can be used outside of the maximum distance the interface moves. This can reduce the number of elements down to 505,296 which will decrease calculation time by over 20%
Figure 7: Comparison of the analysis results with different periods
(Left: 2 seconds, Right: 4 seconds)
The next column will be the last one as for free surface flow analyses. I will introduce an analysis example of a micro scale free surface flow.
＜ 4. Free surface flow analysis III | 6. Free surface flow analysis V ＞ |
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