## Bubble Benchmark

## Verification of the results by the picture norm:

To visually verify the results the following approximate bubble shapes can be used. (The raw data for the bubble shapes can be obtained from the Reference data page.)

- Bubble shapes at the final time (t=3)
- Test case 1
- Test case 2

## Verification of the results by quantitative data:

Since mere visual inspection is not really enough to say anything about the accuracy of the simulations the following benchmark quantities have been defined and computed.

#### Center of Mass

The centroid or center of mass of the bubble is defined by

_{2}denotes the region that the bubble occupies.

- Center of Mass for all groups
- Test Case 1
- Test Case 2

#### Circularity

The "degree of circularity" in can be defined as

Here, P_{a} denotes the perimeter or circumference of a circle with diameter d_{a} which has an area equal to that of a bubble with perimeter P_{b}. For a perfectly circular bubble or drop the circularity will be equal to unity and decrease as the bubble is deformed.

- Circularity for all groups
- Test Case 1
- Test Case 2

#### Rise Velocity

The mean velocity with which a bubble is rising or moving is a particularly interesting quantity since it does not only measure how the interface tracking algorithm behaves but also the quality of the overall solution. The mean bubble velocity is defined as

*Ω*again denotes the region that the bubble occupies.

_{2}- Rise velocity for all groups
- Test case 1
- Test case 2

Continue reading: