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Zbl 0791.76066
Petschek, A.G.; Libersky, L.D.
Cylindrical smoothed particle hydrodynamics. (English)
[J] J. Comput. Phys. 109, No.1, 76-83 (1993). ISSN 0021-9991

Smoothed particle hydrodynamics (SPH) is formulated in two-dimensional axisymmetric coordinates. Starting with a three-dimensional Cartesian representation of SPH, we integrate out the angular component and find a two-dimensional cylindrical description. A smoothed ``particle'' in this formulation becomes a smoothed ``torus''. The hoop stress, resulting from interactions within the toroidal ring, is a natural consequence of the derivation. The formulation has been extended to include the entire stress tensor, not just the pressure, and is therefore applicable to a wide range of materials and flow speeds.

MSC 2000:: *76M25 Other numerical methods
76N10 Compressible fluids, general

Keywords: Lagrangian frame; smoothed ``torus''; hoop stress; stress tensor

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