Swegle, J. W.; Hicks, D. L.; Attaway, S. W. Smoothed particle hydrodynamics stability analysis. (English) Zbl 0818.76071 J. Comput. Phys. 116, No. 1, 123-134 (1995). SPH (smoothed particle hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events. A von Neumann stability analysis of the SPH algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function. The instability is shown to result from an effective stress with a negative modulus (imaginary sound speed) being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm. Cited in 184 Documents MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:stability criterion; second derivative of kernel function; imaginary sound speed; gridless Lagrangian technique; von Neumann stability analysis; stress state; effective stress PDFBibTeX XMLCite \textit{J. W. Swegle} et al., J. Comput. Phys. 116, No. 1, 123--134 (1995; Zbl 0818.76071) Full Text: DOI