This investigation highlights the complexity of error behaviour in SPH, and shows that the roles of both h and Δ x/ h must be considered when choosing particle distributions and smoothing lengths. The meshfree method can be computationally more expensive compared to the well-established FEM. Numerical experiments confirm the theoretical analysis for one dimension, and indicate that the main results are also true in three dimensions. First-order consistent methods are shown to remove this divergent behaviour. When particles are distributed non-uniformly, error can grow as h is reduced with constant Δ x/ h. We then assess how the numerical error is influenced by the time step. if the number of neighbours per particle is increased), error decreases at a rate which depends on the kernel function's smoothness. Abstract: As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH). If Δ x/ h is reduced while maintaining constant h (i.e. For uniformly spaced particles in one dimension, analysis shows that as h is reduced while maintaining constant Δ x/ h, error decays as h 2 until a limiting discretization error is reached, which is independent of h. Truncation error in mesh-free particle methods. Error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length, Δ x/ h. The Smoothed Particle Hydrodynamics (SPH) method has proven useful for. A truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics (SPH) and related first-order consistent methods such as the first-order form of the reproducing kernel particle method.
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