Hybrid formulations of smoothed particle hydrodynamics

In this paper the concept of hybrid methods or flux-limiter methods from the finite difference approach is applied to Smoothed Particle Hydrodynamics (SPH) to obtain improved results in problems which involve shocks. Several variations of the resulting hybrid SPH formulation are discussed and tested against the Riemann shock tube problem. This new technique allows the SPH continuity equation to be used successfully for this test problem. The work described here shows considerable promise and the methods should be further developed.