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This paper presents a general semi-analytic approach for modeling solid boundaries in the SPH method: boundaries are here considered as a material continuum with a suitable distribution of velocity and pressure; their contributions to each term of the SPH mass and momentum equations can be expressed in terms of a suitable integral extended to the part of the sphere of influence of the particle delimited by the boundary surface. Analytical details with reference to a slightly compressible viscous Newtonian fluid in three dimensions are given. The validity of the method is checked by comparing the obtained numerical results with available experimental data in a benchmark flow case.

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