Stability Of Contact Discontinuity Research Articles

Stability of Contact Discontinuity with General Perturbation for the Compressible Navier-Stokes Equations with Reaction Diffusion

In this article,for the compressible Navier-Stokes equations which have reaction diffusion, the stability of contact discontinuities is considered. The new characteristic for the flow is appearance of the divergence between energy gained and lost because of the reaction . In the energy equations,the term related to the mass fraction of the reactant leads to new technical problem. To solve this problem, in terms of the solutions,a new system should be set up. Using the anti-derivative method and the elaborated energy method, we obtain that as long as the general perturbation of the initial datum plane and the strength of the contact wave are properly small, the contact wave is nonlinear and stable. As a byproduct, we can establish the convergence velocity of contact wave.

On the stability of contact discontinuity for Cauchy problem of compress Navier-Stokes equations with general initial data

In this paper, we study the stability of solutions of the Cauchy problem for 1-D compressible Narvier-Stokes equations with general initial data. The asymptotic limit of solution is found, under some conditions. The results in this paper imply the case that the limit function of solution as t→∞ is a viscous contact wave in the sense, which approximates the contact discontinuity on any finite-time interval as the heat conduction coefficients toward zero. As a by-product, the decay rates of the solution for the fast diffusion equations are also obtained. The proofs are based on the elementary energy method and the study of asymptotic behavior of the solution to the fast diffusion equation.

Pointwise Stability of Contact Discontinuity for Viscous Conservation Laws with General Perturbations

The large time asymptotic behavior towards viscous contact waves for a class of systems of viscous conservation laws is studied in this paper for general initial perturbations. The high order deviation of the viscous solutions from the leading order ansatz is estimated pointwisely via the approximate Green function approach. The structural constraint on the left eigenvector belonging to the principal linearly degenerate family used in [13] is removed so that our results hold, in particular, for the one-dimensional compressible Navier–Stokes equations of gas dynamics in both Lagrangian and Eulerian coordinates.

On the Stability of Contact Discontinuity Separating Two Hypersonic Sources

We present the results of direct high resolution numerical modelling of instability of contact discontinuity, separating two hypersonic spatial or plane sources. We found that the used numerical scheme allows to see instability in steady state inviscid non heatconductive flow. The instability development significantly depends on grid resolution, but, at the same, it is in good accordance with the linear theory predictions. When a real dissipative process is taken into account (namely, non-linear thermal conduction), the dependents of unstable solution on the grid resolution dissapears. The last makes it possible to study the physical instability correctly and, in particular, to determine the instability type. The influence of CD curvature on its stability is also discussed which allows to extend the application of the results on wide range astrophysical objects.

Stability of a collisionless contact discontinuity

The stability of a contact discontinuity in a collisionless plasma is examined. It is shown that the discontinuity can become unstable when the pressure component normal to the magnetic field is not continuous across the discontinuity. Even when the system is unstable, the growth rates are very small and unimportant in the context of wave propagation, except when the propagation is almost normal to the field. The instability could, however, lead to the slow dissipation of contact discontinuities in the solar wind and in the day side of the cusp region of the solar wind-magnetosphere boundary.

Stability of contact discontinuity in a strongly radiating gas

A very simple flow—the two-dimensional steady infinite planar contact discontinuity in an inviscid non-heat-conducting gas without chemical reactions—is used as an example to study the effect of irreversible energy transport by radiation on the stability of motion with respect to infinitesimal perturbations of the interface.