Consistent Shepard Interpolation for SPH-Based Fluid Animation

摘要

We present a novel technique to correct errors introduced by the discretizationof a fluid body when animating it with smoothed particle hydrodynamics(SPH). Our approach is based on the Shepard correction, which reduces theinterpolation errors from irregularly spaced data. With Shepard correction,the smoothing kernel function is normalized using the weighted sum ofthe kernel function values in the neighborhood. To compute the correctionfactor, densities of neighboring particles are needed, which themselves arecomputed with the uncorrected kernel. This results in an inconsistent formulationand an error-prone correction of the kernel. As a consequence,the density computation may be inaccurate, thus the pressure forces areerroneous and may cause instabilities in the simulation process.We present aconsistent formulation by using the corrected densities to compute the exactkernel correction factor and, thereby, increase the accuracy of the simulation.Employing our method, a smooth density distribution is achieved, i.e., thenoise in the density field is reduced by orders of magnitude. To show thatour method is independent of the SPH variant, we evaluate our techniqueon weakly compressible SPH and on divergence-free SPH. Incorporatingthe corrected density into the correction process, the problem cannot bestated 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 applied to improve thedensity distribution on rigid bodies when using a well-known rigid-fluidcoupling approach.