From gas dynamics to pressureless gas dynamics

Probabilistic Model Associated with the Pressureless Gas Dynamics

Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and t...

Numerical Approximations of Pressureless and Isothermal Gas Dynamics

We study several schemes of rst or second-order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations. The pressureless gas system is weakly hyperbolic, giving rise to the formation of density concentrations known as delta-shocks. For the isothermal gas system, the innnite speed of expansion into vacuum leads to zero timestep in the Godunov method ...

Beyond pressureless gas dynamics : Quadrature-based velocity moment models

A New Sticky Particle Method for Pressureless Gas Dynamics

We first present a new sticky particle method for the system of pressureless gas dynamics. The method is based on the idea of sticky particles, which seems to work perfectly well for the models with point mass concentrations and strong singularity formations. In this method, the solution is sought in the form of a linear combination of δ-functions, whose positions and coefficients represent loc...

A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations

Abstract. Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savaré. Their proof uses a discrete particle approximation and stability properties for first order differential inclusions. Here we give a more direct proof that relies on a re...