On the Self-similar Diffraction of a Weak Shock into an Expansion Wavefront

@article{Hunter2012OnTS,
  title={On the Self-similar Diffraction of a Weak Shock into an Expansion Wavefront},
  author={John K. Hunter and Allen M. Tesdall},
  journal={SIAM J. Appl. Math.},
  year={2012},
  volume={72},
  pages={124-143}
}
We study an asymptotic problem that describes the diffraction of a weak, self-similar shock near a point where its shock strength approaches zero and the shock turns continuously into an expansion wavefront. An example arises in the reflection of a weak shock off a semi-infinite screen. The asymptotic problem consists of the unsteady transonic small disturbance equation with suitable matching conditions. We obtain numerical solutions of this problem, which show that the shock diffracts… 

Figures from this paper

Diffraction of a shock into an expansion wavefront for the transonic self-similar nonlinear wave system in two space dimensions

We consider a configuration where a planar shock reflects and diffracts as it hits a semi-infinite rigid screen. The diffracted reflected shock meets the diffracted expansion wave, created by the incident

A note on weak shock wave reflection

This work discusses the possibility of reconstructing, both numerically and experimentally, the steady state flow field and shock reflection pattern close to the triple point of von Neumann, Guderley

A note on weak shock wave reflection

This work discusses the possibility of reconstructing, both numerically and experimentally, the steady state flow field and shock reflection pattern close to the triple point of von Neumann, Guderley

On Shock Reflection–Diffraction in a van der Waals Gas

The problem of a weak shock, reflected and diffracted by a wedge, is studied for the two‐dimensional compressible Euler system. Some recent developments are overviewed and a perspective is presented

On weak shock diffraction in real gases

Asymptotic solutions are obtained for the two-dimensional Euler system for real gases with appropriate boundary conditions which describe the diffraction of a weak shock at a right-angled wedge; the

The unsteady transonic small disturbance equation: Data on oblique curves

We propose and solve a new problem for the unsteady transonic small disturbance equation. Data are given for the self-similar equation in a fixed, bounded region of similarity space, where on a

M ay 2 01 4 On weak shock diffraction in real gases

Asymptotic solutions are obtained for the two-dimensional Euler system for real gases with appropriate boundary conditions which describe the diffraction of a weak shock at a right-angled wedge; the

The Problem of Sonic Shock Formation

The equations of compressible ideal gas flow in Eulerian coordinates and simplified models of this flow are studied by many mathematicians, physicists and engineers, because of their rich

References

SHOWING 1-10 OF 22 REFERENCES

Weak shock reflection

We present numerical solutions of a two-dimensional inviscid Burgers equation which provides an asymptotic description of the Mach reflection of weak shocks. In our numerical solutions, the incident,

Potential theory for regular and mach reflection of a shock at a wedge

If a plane shock hits a wedge, a self-similar pattern of reflected shocks travels outward as the shock moves forward in time. The nature of the pattern is explored for weak incident shocks (strength

Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection

Some phenomena involving intersection of weak shock waves at small angles are considered: the focusing of curved fronts at aretes, the transition between regular and irregular reflection of oblique

Weak shock diffraction

HIGH RESOLUTION SOLUTIONS FOR THE SUPERSONIC FORMATION OF SHOCKS IN TRANSONIC FLOW

We present numerical solutions of two problems for the unsteady transonic small disturbance equations whose solutions contain shocks. The first problem is a two-dimensional Riemann problem with

Self-Similar Solutions for the Triple Point Paradox in Gasdynamics

Numerical solutions of a two-dimensional Riemann problem for the com- pressible Euler equations that describes the Mach reflection of weak shock waves are presented, resolving the von Neumann triple point paradox.

The diffraction of blast. I

  • M. Lighthill
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1949
The behaviour of a plane shock, of any strength, travelling along a wall, when it reaches a corner where the wall turns through a small angle δ, is investigated mathematically by use of a linearized

Transverse diffraction of nonlinear waves and singular rays

We derive an asymptotic partial differential equation which describes the diffraction of a weakly nonlinear high frequency wave in a direction transverse to its rays. Special cases of this equation

The diffraction of blast. II

  • M. Lighthill
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1950
The head-on encounter of a plane shock, of any strength, with a solid corner of angle π - δ is investigated mathematically, when δ is small, by a method similar to that of part I. The incident shock

Systems of Conservation Laws: Two-Dimensional Riemann Problems

1 Problems.- 1.0 Outline.- 1.1 Some models.- 1.2 Basic problems.- 1.2.1 Probing problems.- 1.3 Some solutions.- 1.4 von Neumann paradoxes.- 1.5 End notes.- I Basics in One Dimension.- 2