STEADY NAVIER–STOKES–FOURIER SYSTEM WITH SLIP BOUNDARY CONDITIONS

2014 ◽  
Vol 24 (04) ◽  
pp. 751-781 ◽  
Author(s):  
DIDIER JESSLÉ ◽  
ANTONÍN NOVOTNÝ ◽  
MILAN POKORNÝ
Keyword(s):  
Energy Balance ◽  
Total Energy ◽  
Heat Conductivity ◽  
Slip Boundary Condition ◽  
Entropy Inequality ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Weak Formulation ◽  
Slip Boundary ◽  
Total Energy Balance

We consider a problem modeling the steady flow of a compressible heat conducting Newtonian fluid subject to the slip boundary condition for the velocity. Assuming the pressure law of the form p(ϱ, ϑ) ~ ϱγ + ϱϑ, we show (under additional assumptions on the heat conductivity and the viscosity) that for any γ > 1 there exists a variational entropy solution to our problem (i.e. the weak formulation of the total energy balance is replaced by the entropy inequality and the global total energy balance). Moreover, if [Formula: see text] (together with further restrictions on the heat conductivity), the solution is in fact a weak one. The results are obtained without any restriction on the size of the data.

WEAK SOLUTIONS TO EQUATIONS OF STEADY COMPRESSIBLE HEAT CONDUCTING FLUIDS

2010 ◽  
Vol 20 (05) ◽  
pp. 785-813 ◽  
Author(s):  
PIOTR B. MUCHA ◽  
MILAN POKORNÝ
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
Large Data ◽  
Slip Boundary Condition ◽  
Regularity Of Solutions ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Existence Of A Solution ◽  
Slip Boundary

We consider the steady compressible Navier–Stokes–Fourier system in a bounded three-dimensional domain. We prove the existence of a solution for arbitrarily large data under the assumption that the pressure p(ϱ, θ) ~ ϱθ + ϱγ for [Formula: see text] assuming either the slip or no-slip boundary condition for the velocity and the Newton boundary condition for the temperature. The regularity of solutions is determined by the basic energy estimates, constructed for the system.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

scholarly journals Flow of a viscous compressible fluid produced in a circular tube by an impulsive point source

2011 ◽  
Vol 668 ◽  
pp. 100-112 ◽  
Author(s):  
B. U. FELDERHOF ◽  
G. OOMS
Keyword(s):  
Compressible Fluid ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Sudden Impulse

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. An efficient numerical scheme has been developed for the calculation of flow velocity and pressure disturbance as a function of position and time.

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