Global existence of shock front solution to axially symmetric piston problem in compressible flow

2007 ◽  
Vol 59 (3) ◽  
pp. 434-456 ◽  
Author(s):  
Shuxing Chen ◽  
Zejun Wang ◽  
Yongqian Zhang
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Compressible Flow ◽  
Axially Symmetric ◽  
Piston Problem ◽  
Front Solution ◽  
Shock Front Solution

GLOBAL EXISTENCE OF SHOCK FRONT SOLUTIONS TO THE AXIALLY SYMMETRIC PISTON PROBLEM FOR COMPRESSIBLE FLUIDS

2004 ◽  
Vol 01 (01) ◽  
pp. 51-84 ◽  
Author(s):  
SHUXING CHEN ◽  
ZEJUN WANG ◽  
YONGQIAN ZHANG
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Compressible Fluids ◽  
Axially Symmetric ◽  
Piston Problem ◽  
Front Solution ◽  
Glimm Scheme ◽  
Front Solutions ◽  
Shock Front Solution

In this paper, we study the axially symmetric piston problem for compressible fluids when the velocity of the piston is a perturbation of a constant. Under the assumptions that both the velocity of the piston and the density of the gas outside the piston are small, we prove the global existence of a shock front solution by using a modified Glimm scheme.

Asymptotic decay to relaxation shock fronts in two dimensions

2001 ◽  
Vol 131 (6) ◽  
pp. 1385-1410 ◽  
Author(s):  
Hailiang Liu
Keyword(s):  
Shock Front ◽  
Initial Perturbation ◽  
Two Dimensions ◽  
Decay Rates ◽  
Front Solution ◽  
Asymptotic Decay ◽  
Planar Shock ◽  
Spatial Dimensions ◽  
Shock Front Solution ◽  
Shock Fronts

We prove nonlinear stability of planar shock fronts for certain relaxation systems in two spatial dimensions. If the subcharacteristic condition is assumed and the initial perturbation is sufficiently small and the mass carried by the perturbations is not necessarily finite, then the solution converges to a shifted planar shock front solution as time t ↑ ∞. The asymptotic phase shift of shock fronts is, in general, non-zero and governed by a similarity solution to the heat equation. The asymptotic decay rate to the shock front is proved to be t−1/4 in L∞(R2) without imposing extra decay rates in space for the initial perturbations. The proofs are based on an elementary weighted energy analysis to the error equation.

Modified Governing Equations for Unsteady Compressible Flow in Ducts

1978 ◽  
Vol 45 (4) ◽  
pp. 723-726 ◽  
Author(s):  
A. Celmin¸sˇ
Keyword(s):  
Compressible Flow ◽  
Power Law ◽  
Unsteady Flows ◽  
Tube Flow ◽  
Axially Symmetric ◽  
Governing Equations ◽  
Flow Equations ◽  
Circular Tubes ◽  
First Order ◽  
General Conservation

Conventional governing equations for unsteady compressible tube flows are reviewed and it is shown that they neglect first-order terms which can have significant magnitudes. The derivation of correct tube flow equations from general conservation laws is demonstrated for the case of axially symmetric straight tubes. The traditionally neglected terms are computed explicitly for unsteady flows with power law profiles through circular tubes.

scholarly journals A multidimensional piston problem for the Euler equations for compressible flow

2005 ◽  
Vol 13 (2) ◽  
pp. 361-383 ◽  
Author(s):  
Shuxing Chen ◽  
◽  
Gui-Qiang Chen ◽  
Zejun Wang ◽  
Dehua Wang ◽  
...  
Keyword(s):  
Compressible Flow ◽  
Euler Equations ◽  
Piston Problem
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