Adaptive kernel estimation and SPH tensile instability

We propose an alternative method to remove the tensile instability in standard SPH simulations of a fluid. The method relies on an adaptive density kernel estimation (ADKE) algorithm, which allows the width of the kernel interpolant to vary locally in such a way that only the minimum necessary smoothing is applied to the data. By means of a linear perturbation analysis of the SPH equations for a heat-conducting, viscous, van der Waals fluid, we derive the corresponding dispersion relation. Solution of the dispersion relation in the short wavelength limit shows that the tensile instability is effectively removed for a wide range of the ADKE parameters. Application of the method to the formation of equilibrium liquid drops confirms the analytical results of the linear stability analysis. Examples of the resolving power of the method are also given for the nonlinear oscillations of an excited drop and the Sedov blast wave problem.