## 1 Introduction
### Problem Statement  
Before entering into the details of the problem statement, the following summarizes the shortcomings of the prior technique for realistically simulating foam patterns:  
1. Foam patterns are generated only by the depth-based curvature difference, not by water flow. 2. While this does not appear to be a mask map, it is difficult to depict detailed foam motion for reasons (1). 3. It's particularly challenging to convey the complexity of foam, which is largely dependent on water velocity, such as the movement of a bubble being drawn in. In general, secondary effects such as foam are based on the motion of water particles. Among the various secondary effects, foam particles not only have intrinsic patterns, but also exhibit dynamic and complex movements compared to water particles. Since it is strongly linked to the underlying water simulation, if there is little movement of the water particles, the foam particles are clumped. However, if the turbulence of water particles is strongly applied to express the foam effect, the water flow itself is severely deformed. [PERSON] et al. proposed a curvature-based clamping function to alleviate the clumping problem of foam [26; 27] (see Figure 1). As shown in Figure 1, intrinsic patterns of foam can be expressed using depth-based curvature flow, but like a mask map, it only affects the foam generation process, so the movement of foam particles still depends only on the underlying water. Recently, [PERSON] and [PERSON] proposed a technique of advection according to the type of foam by dividing it into wave and surface [26]. They expressed a cloud-like surface foam by adding a spring force such as SPH, but still rely on the underlying water motion. Figure 2 shows the results of the previous techniques that modeled foam patterns based on curvature in more detail, and the wave patterns shown in the red line of Figure 1 are shown as a chart. In the technique of [PERSON] et al., foam patterns were modeled by dividing the area where the foam particles would be generated and the area where the foam particles would not be generated [26; 27]. As a result, foam particles are generated in the areas where values exist in the upper part of Figure 2, and they are not generated in the 'No foam particles' area. As mentioned earlier, this is a weight in the same way  
as the mask map, and this value does not affect the foam advection and only maintains the foam pattern. In other words, it has no effect on the movement of the foam particles. To address these issues, this paper proposes a method to enhance the advection of foam particles by calculating angular momentum from water particles, which are the underlying fluids. To implement the proposed method, the following sub-problems must be solved from the input water particles:  
1. Calculation of angular momentum from water particles. Tuning the motion of the underlying fluids whenever controlling the foam effects is a very cumbersome task, and as a result, it becomes difficult to model the scene in the manner in which the user desires. Therefore, we calculate the angular momentum to advect the foam particles without affecting the position of the water particles. 2. Advection of foam particles reflecting angular momentum. We reliably advect the foam particles using the angular momentum calculated from the water particle. 3. Integration with existing foam effects techniques. Foam particles with angular momentum are integrated into the foam generation framework of existing techniques. With the first sub-problem we can calculate the angular velocity from the water particles. This process should be able to maintain angular momentum by integrating the force without affecting the position of the water particles. This process calculates the force for advection of the foam particles. It should be able to maintain angular momentum by integrating the force without affecting the position of the water particles. Through the second sub-problem, the foam particles are advected based on the angular velocity.