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Smoothed particle hydrodynamics stability analysis. (English) Zbl 0818.76071
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.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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