# Presentation

Consistent Shepard Interpolation for SPH-Based Fluid Animation

Event Type

Technical Papers Fast-Forward

TimeSunday, 17 November 201918:47 - 18:48

LocationGreat Hall 1&2

DescriptionWe present a novel technique to correct errors introduced by the discretization of a fluid body when animating it with smoothed particle hydrodynamics (SPH). Our approach is based on the Shepard correction, which reduces the interpolation errors from irregularly-spaced data. With Shepard correction, the smoothing kernel function is normalized using the weighted sum of the kernel function in the neighborhood. To compute the correction factor, densities of neighboring particles are needed, which themselves are computed with the uncorrected kernel. This results in an inconsistent formulation and an error-prone correction of the kernel. As a consequence, the density computation may be inaccurate, thus the pressure forces are erroneous and may cause instabilities in the simulation process. We present a consistent formulation by using the corrected densities to compute the exact kernel correction factor and, thereby, increase the accuracy of the simulation. Employing our method, a smooth density distribution is achieved, i.e., the noise in the density field is reduced by orders of magnitude (see Figure 1, left and center). Besides that, we decrease the overall volume loss of the simulated fluid. To show that our method is independent of the SPH-Variant, we evaluate our method on weakly compressible SPH and on divergence-free SPH. Incorporating the corrected density into the correction process, the problem cannot be stated explicitly anymore. We propose an efficient and easy to implement algorithm to solve the implicit problem by applying the power method. Additionally, we demonstrate how our model can be used to improve the density distribution on rigid bodies when using a well-known rigid-fluid coupling approach.