On the Properties of a Quasihydrodynamic System of Equations for a Homogeneous Gas Mixture with a Common Regularizing Velocity View Full Text


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Article Info

DATE

2022-03

AUTHORS

A. A. Zlotnik, A. S. Fedchenko

ABSTRACT

We study a quasihydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions with a common regularizing velocity. For this system, we derive an entropy balance equation with nonnegative entropy production in the presence of diffusion fluxes of the mixture components. In the absence of diffusion fluxes, a system of equations linearized on a constant solution is constructed in a new way. This system is reduced to a symmetric form, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2 $$\end{document}-dissipativity of its solutions is proved, and the degeneracy (with respect to the densities of the mixture components) of the parabolic property of the original system is established. In fact, the system under study has a composite type. The obtained properties mathematically rigorously reflect its physical well-posedness and the dissipative nature of quasihydrodynamic regularization. More... »

PAGES

341-356

References to SciGraph publications

  • 2009. Quasi-Gas Dynamic Equations in NONE
  • 2008-06. Parabolicity of a quasihydrodynamic system of equations and the stability of its small perturbations in MATHEMATICAL NOTES
  • 2010-04-25. Quasi-gasdynamic system of equations with general equations of state in DOKLADY MATHEMATICS
  • 1999. Multicomponent Flow Modeling in NONE
  • 2021-01-16. On a New Spatial Discretization for a Regularized 3D Compressible Isothermal Navier–Stokes–Cahn–Hilliard System of Equations with Boundary Conditions in JOURNAL OF SCIENTIFIC COMPUTING
  • 2014-11. On quasi-gasdynamic and quasi-hydrodynamic equations for binary gas mixtures in DOKLADY MATHEMATICS
  • 2018-05. Quasi-Hydrodynamic Model of Multiphase Fluid Flows Taking into Account Phase Interaction in JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS
  • 2019-11. Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2010-10. Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations in DOKLADY MATHEMATICS
  • 2008-03. Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
  • 2021-01. Numerical Simulation of Gas Mixtures Based on the Quasi-Gasdynamic Approach as Applied to the Interaction of a Shock Wave with a Gas Bubble in COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1134/s00122661220300053

    DOI

    http://dx.doi.org/10.1134/s00122661220300053

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