CYLINDRICAL SMOOTHED PARTICLE HYDRODYNAMICS

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. No pathological behavior is observed at the symmetry axis. 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. Three calculations are presented and compared to known results. © 1993 by Academic Press, Inc.