I. Karafyllis and M. Papageorgiou, “A particle method for 1‐D compressible fluid flow,” Stud. Appl. Math., 2023, doi: 10.1111/sapm.12623.
https://doi.org/10.1111/sapm.12623
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.