DOI: 10.1111/sapm.12623 ISSN: 0022-2526
A particle method for 1‐D compressible fluid flow
Iasson Karafyllis, Markos Papageorgiou- Applied Mathematics
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.