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Grid Uniformity Effects on Surface Tension Modeling

A very useful and powerful capability in FLOW-3D is the ability to use non-uniform, or stretched computational grids. Stretching the grid allows resolution to be reduced in a particular direction when gradients in that direction are small. Conversely, resolution can be increased in regions with high gradients. This stretching of the grid may reduce runtime and memory usage when used appropriately. While there is no limit to the cell aspect ratio, high cell aspect ratios can create convergence problems that may require an ADI pressure solver be activated.

Stretched grids are generally not recommended when surface tension is activated and the free surface moves through the non-uniform regions of the grid. As a general rule of thumb, cell aspect ratios should be limited to about 1.5 in these cases. The more uniform the grid, the more accurately the free surface curvature can be computed. The following example will demonstrate this.

Let's say we are simulating a droplet of water that is 1 mm in diameter moving at 100 cm/sec. To determine the importance of surface tension in the simulation, we evaluate the Weber number, which represents the ratio of inertia to surface tension. The Weber number is approximately 10, so surface tension forces are significant.

In the first simulation, a uniform grid with a spacing of 0.01 cm is used. Figure 1 shows the droplet moving through the grid relatively smoothly. In the second simulation, the grid is stretched by a factor of 3 in the direction of motion. Figure 2 shows how the droplet quickly becomes distorted and breaks up. The distortion is primarily due to surface perturbations created by inaccuracies in surface curvature calculation on a coarse, non-uniform grid. Increasing the resolution significantly while maintaining the stretching delays the distortion but, eventually, the droplet still breaks up.

As noted earlier, the calculation of surface tension curvature is most accurate when a uniform mesh is used. One way to easily add a uniform grid to a simulation without entirely re-meshing is to place a Nested Grid over the region where the free surface passes. Figure 3 shows the result of overlaying a uniform nested grid on a portion of the droplet's path. While the droplet is moving through the nested grid, its motion is smooth and its shape is maintained well. Once the droplet leaves the nested grid and begins moving through the stretched mesh, it becomes distorted.

Clearly, a uniform grid provides the most accurate results when surface tension is significant. A simple way to easily and selectively add a uniform grid is by using a Nested Grids.

Reducing Memory Usage via Single Precision

One of the challenges that CFD users must occasionally tackle is keeping their computational grid small enough to fit in memory (RAM). Often, though, users are faced with problems that are either exceedingly complex or physically large, and so require large computational grids. The larger the grid, the more memory must be allocated. If the amount of required memory exceeds the available RAM, the solver will begin to swap to the hard drive and machine performance will slow to a crawl.

One solution to this problem is to purchase more memory. However, the maximum addressable memory on 32-bit hardware using Windows or Linux is 2 GB. This limits the grid size to about 4-5 million cells, depending on the physical models activated. An alternative to buying more memory is to select FLOW-3D's Single Precision version through the Preferences, Runtime menu This will typically reduce the memory requirements by about 40%, allowing much larger simulations to be run.