However, a constant smoothing length has its own disadvantages owing to the lack of adaptiveness. For these reasons, a constant support radius with an appropriate length (usually two to four times the particle radius) is usually chosen for these simulations. Increasing the number of neighbors improves the accuracy, but at the cost of an exponential increase in the computational overhead. It is clear that the interpolation accuracy decreases when there are too few neighbors.

One of the main factors affecting the SPH interpolation accuracy is the smoothing length (i.e., the support radius of the smoothing kernel), which determines the number of neighboring particles involved in the interpolation. In SPH, the accuracy of interpolation is important for maintaining the stability and realism of the corresponding fluid simulations. By storing the information about the particles’ physical quantities, computational resources focus on relevant fluid regions hence, the simulation efficiency of SPH is usually higher than that of Eulerian grid-based methods. The physical quantities (e.g., density and velocity) at any location are interpolated using the neighboring fluid particles within a given distance. As a Lagrangian particle-based method, SPH discretely samples a fluid into a group of particles. Physics-based fluid simulation technologies, such as smoothed particle hydrodynamics (SPH), have been widely applied in feature films and computer games.

Fluid simulations are important in computer graphics.

Smoothed particle hydrodynamics book