D. Asprone1, F. Auricchio2, G. Manfredi1, A. Prota1, A. Reali2, G. Sangalli3
CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.062.001
Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative of given functions, as well… More >
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