A PID Algorithm from Explicit Parameters to Implicit Parameters for SPH Simulation

Simulation is generally based on physical parameters to obtain the corresponding visual effect, such as setting viscosity to simulate the fluid movement speed, setting surface tension parameter to simulate the droplet size when the droplet splashes, etc. This kind of simulation is called Forward Simulation (FS). However, sometimes it is often necessary to adjust parameters to achieve a specific visual effect, such as calculating the viscosity parameter of the fluid so that the fluid can achieve the set flow rate of 10cm/s, calculating the surface tension parameter so that the radius of the splashing droplet can achieve the set 1mm, etc. This kind of simulation is called Reverse Parameter Simulation (RS). This paper proposes an adaptive algorithm to calculate RS based on PID (Proportional Integral Derivative) method. This method calculates the explicit parameters through FS and adjusts the implicit parameters through adaptive feedback to achieve RS. After that, we realized the migration of droplets with different wetting properties. This RS method used to calculate implicit parameters has great application potential. For example, it can be used for visual simulation with specific needs, identification of unknown material properties, or simulation of some complex chemical processes (such as electro-wetting process), etc.