A Particle Method for 1-D Compressible Fluid Flow

TL;DR

This paper introduces a new particle scheme for 1-D viscous compressible fluid flow that ensures convergence to weak solutions and preserves key physical inequalities, serving as both a numerical and theoretical tool.

Contribution

It presents a novel particle method that guarantees convergence and preserves physical inequalities, aiding in both simulation and existence proofs for compressible fluids.

Findings

The particle scheme converges to weak solutions of the Navier-Stokes equations.

Mass conservation and energy decay are maintained by the method.

The method can be used for numerical simulation and existence proofs.

Abstract

This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities that hold for the fluid model are preserved by the particle method: mass is conserved, mechanical energy is decaying, and a modified mechanical energy functional is also decaying. The proposed particle method can be used both as a numerical method and as a method of proving existence of solutions for compressible fluid models.