Advances in Non-equilibrium Fluid Mechanics: Theory, Analysis, and Simulations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 790

Special Issue Editors


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Guest Editor
Faculty of Physics, Moscow State University, 1-2 Leninskie Gory, Moscow, 119991, Russia
Interests: non-equilibrium fluid dynamics; rarefied gas dynamics; kinetic theory; shock waves; micro-channel flows

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Guest Editor
Kutateladze Institute of Thermophysics of Siberian Branch of the Russian Academy of Sciences, Lavrentyev Ave. 1, Novosibirsk, 630090, Russia
Interests: rarefied gas dynamics; direct simulation Monte Carlo; pulsed laser ablation; computational fluid dynamics

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Guest Editor
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia
Interests: computational fluid dynamics; numerical analysis; parallel computing; computational physics; rarefied gas dynamics
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Special Issue Information

Dear Colleagues,

The non-equilibrium of a flow is caused by physical and chemical processes occurring at different scales. The possibility of a detailed description of non-equilibrium fluid flows is of decisive importance, both for various engineering fields and for solving fundamental problems. The simulation of such flows is a multi-disciplinary problem encompassing molecular physics, chemistry, gas dynamics, thermodynamics and mathematics.

The goal of this Special Issue is to publish original research and review articles covering the applications of various mathematical models and describing the development of numerical methods to simulate non-equilibrium fluid dynamic processes.

Topics of interest include, but are not limited to, the following:

  • Boltzmann and Model Kinetic Equations
  • Direct Simulation Monte Carlo
  • Mesoscale and Multiscale Modeling
  • Micro- & Nanoscale Flows
  • Multiphase Flows
  • Non-equilibrium Reacting Flows
  • Plasma Flows and Processes
  • Supersonic Flows and Shock Waves
  • Rarefied Gas Flows and Vacuum Technologies.

Dr. Maksim Timokhin
Dr. Alexey A. Morozov
Dr. Vladimir Titarev
Guest Editors

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Published Papers (1 paper)

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Research

30 pages, 1936 KiB  
Article
Two-Dimensional System of Moment Equations and Macroscopic Boundary Conditions Depending on the Velocity of Movement and the Surface Temperature of a Body Moving in Fluid
by Auzhan Sakabekov, Yerkanat Auzhani and Shinar Akimzhanova
Mathematics 2024, 12(10), 1491; https://doi.org/10.3390/math12101491 - 10 May 2024
Viewed by 303
Abstract
This article is dedicated to the derivation of a two-dimensional system of moment equations depending on the velocity of movement and the surface temperature of a body submerged in fluid, and macroscopic boundary conditions for the system of moment equations approximating the Maxwell [...] Read more.
This article is dedicated to the derivation of a two-dimensional system of moment equations depending on the velocity of movement and the surface temperature of a body submerged in fluid, and macroscopic boundary conditions for the system of moment equations approximating the Maxwell microscopic boundary condition for the particle distribution function. The initial-boundary value problem for the Boltzmann equation with the Maxwell microscopic boundary condition is approximated by a corresponding problem for the system of moment equations with macroscopic boundary conditions. The number of moment equations and the number of macroscopic boundary conditions are interconnected and depend on the parity of the approximation of the system of moment equations. The setting of the initial-boundary value problem for a non-stationary, nonlinear two-dimensional system of moment equations in the first approximation with macroscopic boundary conditions is presented, and the solvability of the above-mentioned problem in the space of functions continuous in time and square-integrable in spatial variables is proven. Full article
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