Cylindrical smoothed particle hydrodynamics. (English) Zbl 0791.76066

Petschek, A. G.; Libersky, L. D.

J. Comput. Phys. 109, No. 1, 76-83 (1993).

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:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

Lagrangian frame; smoothed “torus”; hoop stress; stress tensor