A particle method for 1-D compressible fluid flowA particle method for 1-D compressible fluid flow Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2024-06-282023enThis 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.The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 Research and Innovation programme/ ERC Grant Agreement n. [833915], project TrafficFluid.http://creativecommons.org/licenses/by-nc-nd/4.0/Studies in Applied Mathematics15141282-1331Karafyllis and Papageorgiou_Stud. Appl. Math._2023_manuscript.pdfChania [Greece]Library of TUC2024-06-25application/pdf552.5 kBfree Karafyllis Iason Καραφυλλης Ιασων Papageorgiou Markos Παπαγεωργιου Μαρκος Wiley Particle methods Compressible fluid flow