Zero dissipation limit to contact discontinuity for the compressible navier-stokes system of general gas

2016 ◽  
Vol 36 (1) ◽  
pp. 157-172 ◽  
Author(s):  
Hakho HONG
Keyword(s):  
Stokes System ◽  
Contact Discontinuity ◽  
Navier Stokes

scholarly journals Redistribution of Energy during Interaction of a Shock Wave with a Temperature Layered Plasma Region at Hypersonic Speeds

Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 326
Author(s):  
O. A. Azarova ◽  
T. A. Lapushkina ◽  
K. V. Krasnobaev ◽  
O. V. Kravchenko
Keyword(s):  
Energy Source ◽  
Shock Wave ◽  
Mach Number ◽  
Stokes System ◽  
Contact Discontinuity ◽  
Volume Density ◽  
Navier Stokes ◽  
Plasma Region ◽  
Specific Internal Energy ◽  
Hypersonic Speeds

The paper is devoted to the problem of the interaction between a shock wave and a thermally stratified energy source for the purpose of supersonic/hypersonic flow control realization. The effect of the thermally stratified energy source on a shock wave with the Mach number in the range of 6–12 is researched numerically based on the Navier-Stokes system of equations. Redistribution of specific internal energy and volume density of kinetic energy behind the wave front is investigated. Multiple manifestations of the Richtmyer-Meshkov instability has been obtained which has caused the blurring and disappearance of shock wave and contact discontinuity fronts in density fields. A study of the efficiency of using a stratified energy source instead of a homogeneous one with the same value of the full energy is carried out. The agreement with the available experimental data for the shock wave Mach number 6 has been obtained.

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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