A new sticky particle method for pressureless gas dynamics
We present a new sticky particle method for the system of pressureless gas dynamics. The method is based on the idea of sticky particles The particle velocities are approximated in a special way using certain reconstruction technique, which leads to reasonable gluing procedure in 2-D case. We show that our particle approximation satisfies the original system of pressureless gas dynamics in a weak sense, but only within a certain residual, which is rigorously estimated. We also explain why the relevant errors should diminish as the total number of particles increases and confirm this by extensive numerical testing.
Mathematical problems and theory of numerical methods