scholarly journals Zero viscosity and thermal diffusivity limit of the linearized compressible Navier–Stokes–Fourier equations in the half plane

2021 ◽  
pp. 1-40
Author(s):  
Yutao Ding ◽  
Ning Jiang
Keyword(s):  
Approximate Solution ◽  
Thermal Diffusivity ◽  
Half Plane ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Viscous Layer ◽  
Initial Boundary Problem ◽  
Zero Viscosity ◽  
Appl Math

We study the zero viscosity and thermal diffusivity limit of an initial boundary problem for the linearized Navier–Stokes–Fourier equations of a compressible viscous and heat conducting fluid in the half plane. We consider the case that the viscosity and thermal diffusivity converge to zero at the same order. The approximate solution of the linearized Navier–Stokes–Fourier equations with inner and boundary expansion terms is analyzed formally first by multiscale analysis. Then the pointwise estimates of the error terms of the approximate solution are obtained by energy methods. Thus establish the uniform stability for the linearized Navier–Stokes–Fourier equations in the zero viscosity and heat conductivity limit. This work is based on (Comm. Pure Appl. Math. 52 (1999), 479–541) and generalize their results from isentropic case to the general compressible fluid with thermal diffusive effect. Besides the viscous layer as in (Comm. Pure Appl. Math. 52 (1999), 479–541), the thermal layer appears and couples with the viscous layer linearly.

scholarly journals Solvability of a problem for the equations of dynamics of one-temperature mixtures of heat-conducting viscous compressible fluids

2019 ◽  
Vol 486 (2) ◽  
pp. 159-162
Author(s):  
A. E. Mamontov ◽  
D. A. Prokudin
Keyword(s):  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Natural Generalization ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Component Mixture ◽  
Initial Boundary Value ◽  
Fourier Model

A system of partial differential equations governing the three-dimensional unsteady flow of a homogeneous two-component mixture of heat-conducting viscous compressible fluids (gases) is considered within the multivelocity approach. The model is complete in the sense that it retains all terms in the equations, which are a natural generalization of the Navier-Stokes-Fourier model for the motion of a single-component medium. The existence of weak solutions to the initial-boundary value problem describing the flow in a bounded domain is proved globally in time and the input data.

scholarly journals Calculation of gas flow rates in concentrated fire vortices

2019 ◽  
pp. 108-114
Author(s):  
A. G. Obukhov ◽  
L. I. Maksimov
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Local Heating ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Heat Conducting

The article presents the results of numerical simulation of the generation of free fire vortices in the laboratory without the use of special twisting devices. A. Yu. Varaksin, the corresponding member of the Russian Academy of Sciences, in his experimental studies has described the principal possibility of physical modeling of the occurrence of concentrated fire vortices.  In the model of a compressible continuous medium for the complete system of Navier — Stokes equations, an initial-boundary value problem has been proposed that describes complex three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling heat flows. We has constructed approximate solutions of the complete Navier — Stokes system of equations and has determined velocity characteristics of threedimensional unsteady gas flows initiated by local heating of the underlying surface by nineteen heat sources, using explicit difference schemes and the proposed initial-boundary conditions.  

3-D flow of a compressible viscous micropolar fluid model with spherical symmetry: A brief survey and recent progress

2018 ◽  
Vol 30 (01) ◽  
pp. 1830001 ◽  
Author(s):  
Ivan Dražić
Keyword(s):  
Spherical Symmetry ◽  
Micropolar Fluid ◽  
Boundary Data ◽  
Fluid Model ◽  
Initial Density ◽  
Initial Boundary ◽  
Generalized Solution ◽  
Heat Conducting ◽  
Initial Boundary Problem ◽  
Concentric Spheres

We consider the non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data. In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initial-boundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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