where [p.sub.i] is the pressure at particle i, k is a stiffness parameter to allow small density fluctuation, [[rho].sub.0] is the reference density, and [gamma] is a user defined value which is usually set to 1 for SPH and 7 for WCSPH.
In standard WCSPH, the physical quantities of all particles are being traced and updated at each time step to obtain a correct and stable simulation, whereas this is not always necessary in terms of visual plausibility.
In this section, we present several scenes simulated with our sleepy method in the context of WCSPH, which show that our algorithm can obtain similar visual results and is more efficient than standard WCSPH.
This example is created using sleepy WCSPH together with boundary handling methods from [11, 32].
In Figure 4, we make a visual comparison between the final effects with and without our repulsive force model based on sleepy WCSPH. From the figures we can see that the tensile instability issue is avoided and surface tension like visual effects is obtained as well as the particle distribution has been improved due to the proposed repulsive force model.