The dynamics of pressureless dust clouds and delta waves

The equations of isothermal gas dynamics are studied in the limit when the sound speed vanishes, giving the so-called pressureless gas equations. The collision of two clouds of dust is modeled with these equations in the case where the clouds have finite extent and are surrounded by vacuum. The delta shock that arises in the initial stage of the collision evolves into a delta rarefaction-shock and then into a delta double-rarefaction as first one cloud and then the other is fully accreted into the singularity. A high-resolution finite volume method that captures this behavior is also presented and numerical results shown.