Lagrangian Particle Method for Compressible Fluid Dynamics
  A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwinding second-order particle-based algorithm with limiter, providing accuracy and long term stability, (c) elimination of the dependence on artificial parameters such as the smoothening length in SPH, causing difficulties in the case of large density changes, and (d) accurate resolution of states at free interfaces. Numerical verification test demonstrating the convergence order are presented as well as examples of complex free surface flows. 
Hsin-Chiang Chen, Roman Samulyak, Wei Li
math.NA