Measurement of the shock profiles with streak technique and different detonating arrangements

In the present work, we study the normal shock wave flow problem using a combination of the OBurnett equations and the Holian conjecture. The numerical results of the OBurnett equations for normal shocks established several fundamental aspects of the equations such as the thermodynamic consistency of the equations, and the existence of the heteroclinic trajectory and smooth shock structures at all Mach numbers. The shock profiles for the hydrodynamic field variables were found to be in quantitative agreement with the direct simulation Monte Carlo (DSMC) results in the upstream region, whereas further improvement was desirable in the downstream region of the shock. For the discrepancy in the downstream region, we conjecture that the viscosity–temperature relation (μ∝Tφ) needs to be modified in order to achieve increased dissipation and thereby achieve better agreement with the benchmark results in the downstream region. In this respect, we examine the Holian conjecture (HC), wherein transport coefficients (absolute viscosity and thermal conductivity) are evaluated using the temperature in the direction of shock propagation rather than the average temperature. The results of the modified theory (OBurnett + HC) are compared against the benchmark results and we find that the modified theory improves upon the OBurnett results, especially in the case of the heat flux shock profile. We find that the accuracy gain is marginal at lower Mach numbers, while the shock profiles are described better using the modified theory for the case of strong shocks.

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A survey on stability of viscous shock profiles without genuine nonlinearity

Nonlinear Evolutionary Partial Differential Equations - AMS/IP Studies in Advanced Mathematics ◽

10.1090/amsip/003/27 ◽

1996 ◽

pp. 319-332

Keyword(s):

Shock Profiles ◽

Genuine Nonlinearity

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STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202595000188 ◽

1995 ◽

Vol 05 (03) ◽

pp. 279-296 ◽

Cited By ~ 9

Author(s):

MING MEI

Keyword(s):

Conservation Laws ◽

Decay Rates ◽

Asymptotically Stable ◽

Time Decay ◽

Shock Condition ◽

Viscous Conservation Laws ◽

Time Decay Rates ◽

Shock Profiles ◽

Degenerate Shock ◽

The Stability

This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.

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