A particle method for 1‐D compressible fluid flow

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