Weak Serrin-type blowup criterion for three-dimensional nonhomogeneous viscous incompressible heat conducting flows

2020 ◽  
Vol 402 ◽  
pp. 132203
Author(s):  
Yongfu Wang
Keyword(s):  
Three Dimensional ◽  
Heat Conducting ◽  
Blowup Criterion

scholarly journals MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

2017 ◽  
pp. 93-98
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Gas Flow ◽  
Local Heating ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Point Of View ◽  
Underlying Surface ◽  
Heat Conducting ◽  
Gas Dynamics Equations ◽  
Viscous Heat ◽  
Flow Formation

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

scholarly journals PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

scholarly journals NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING

2015 ◽  
pp. 87-93
Author(s):  
E. M. Sorokina ◽  
A. G. Obukhov
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Boundary Condi Tions ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Condi Tions

To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

scholarly journals METHOD OF PARALLELIZATION OF NUMERICAL ALGORITHMOF NAVIER-STOKES EQUATIONS COMPLETE SYSTEM

2016 ◽  
pp. 92-98
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Thermal Conductivity ◽  
Gas Flow ◽  
Stokes Equations ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Computation Time ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Comparison Of The Results

The article considers the features of numerical construction of solutions of the Navier-Stokes equations full system describing a three-dimensional flow of compressible viscous heat-conducting gas under the action of gravity and Coriolis forces. It is shown that accounting of dissipative properties of viscosity and thermal conductivity of the moving continuum, even with constant coefficients of viscosity and thermal conductivity, as well as the use of explicit difference scheme calculation imposes significant restrictions on numerical experiments aimed at studying the arising complex flows of gas or liquid. First of all, it is associated with a signifi- cant complication of the system of equations, the restrictions on the value of the calculated steps in space and time, increasing the total computation time. One of the options is proposed of algorithm parallelization of numerical solution of the complete Navier - Stokes equations system in the vertical spatial coordinate. This parallelization option can significantly increase the computing performance and reduce the overall time of counting. A comparison of the results of calculation of one of options of gas flow in the upward swirling flow obtained by serial and parallel programs is presented.

scholarly journals Global Existence of the Three Dimensional Heat-conductive Incompressible Viscous Fluids

2018 ◽  
Vol 179 ◽  
pp. 01001
Author(s):  
Jie Wu
Keyword(s):  
Cauchy Problem ◽  
Heat Conductivity ◽  
A Priori Estimates ◽  
Three Dimensional ◽  
Global Solutions ◽  
Local Solution ◽  
Viscous Fluids ◽  
Heat Conducting ◽  
The Cauchy Problem ◽  
Incompressible Viscous Fluids

In this paper, we consider the Cauchy problem of non-stationary motion of heatconducting incompressible viscous fluids in ℝ3. About the heat-conducting incompressible viscous fluids, there are many mathematical researchers study the variants systems when the viscosity and heat-conductivity coefficient are positive. For the heat-conductive system, it is difficulty to get the better regularity due to the gradient of velocity of fluid own the higher order term. It is hard to control it. In order to get its global solutions, we must obtain the a priori estimates at first, then using fixed point theorem, it need the mapping is contracted. We can get a local solution, then applying the criteria extension. We can extend the local solution to the global solutions. For the two dimensional case, the Gagliardo-Nirenberg interpolation inequality makes use of better than the three dimensional situation. Thus, our problem will become more difficulty to handle. In this paper, we assume the coefficient of viscosity is a constant and the coefficient of heat-conductivity satisfying some suitable conditions. We show that the Cauchy problem has a global-in-time strong solution (u,θ) on ℝ3 ×(0, ∞).

Solvability of unsteady equations of three-dimensional motion of heat-conducting viscous compressible bifluids

2021 ◽  
Vol 85 (4) ◽  
Author(s):  
Alexander Evgenievich Mamontov ◽  
Dmitry Alekseevich Prokudin
Keyword(s):  
Three Dimensional ◽  
Heat Conducting

Numerical simulation of complex gas flows in concentrated fire vortices

2019 ◽  
Vol 5 (3) ◽  
pp. 47-68
Author(s):  
Sergei P. Bautin ◽  
Alexandr G. Obukhov
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Local Heating ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Gas Flows ◽  
Heat Conducting ◽  
Russian Academy Of Sciences ◽  
Academy Of Sciences

This article presents the results of numerical simulation of free fire vortices arising in laboratory conditions. The authors demonstrate the possibility of obtaining such concentrated fire vortices in a series of experimental studies conducted under the supervision of A. &nbsp;Yu. &nbsp;Varaksin, a corresponding member of the Russian Academy of Sciences, at the Joint Institute for High Temperatures of the Russian Academy of Sciences.<br> The authors propose to consider the analytical and numerical studies of arising complex swirling gas flows during local heating of a metal underlying surface by several sources from the point of view of gas dynamics. When considering complex flows of a heating gas as a motion of a viscous, heat-conducting, and compressible continuous medium, the complete system of Navier&nbsp;— Stokes equations is used. The proposed initial-boundary conditions made it possible to numerically determine the main gas-dynamic characteristics of the resulting three-dimensional and unsteady gas flows in free fire vortices.<br> The calculation results showed that during the formation of fiery vortices, several stages are distinguished in their development. The first stage is characterized by the occurrence of local gas flows diverging in the radial direction from the heating regions. The second stage is accompanied by the formation in the regions of the location of the heating sources of local vortices with opposite spin directions. The third stage is characterized by the fact that from smaller vortices due to the intense influx of external air a common large thermal vortex is formed, which receives a positive twist under the influence of the Coriolis force. At the fourth stage, with an increase in the rotation speed, a decrease in the vertical dimensions of the thermal vortex and its decay into several small ones is observed. Thus, the completion of the life cycle of one concentrated vortex is replaced by the formation of a new one. For the initial parameters, the lifetime of the concentrated thermal vortex is about one minute.

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