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.

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