Propagation of non-planar weak and strong shocks in a non-ideal relaxing gas

Shah, Sarswati; Singh, Randheer

doi:10.1007/s11587-019-00472-w

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…where Ω = (m∕x) x=X and v = u s − Π. With the help of equations ( 6), (9), and (10) (2,3) , we get the nonlinear differential equation describing the shock strength [u] as…”

Section: Evolution Equation For Shock Progressionmentioning

confidence: 99%

“…After the developments of ideal theory, many authors extended the propagation of growth and decay behavior of converging and diverging shocks in non‐ideal distinct mediums (one may see [7] to [8]). Shah and Singh investigated the propagation of weak and strong shocks in a non‐ideal relaxing gas in [9] and the profiles of imploding shocks in [10] and also determined the evolution equation for singular surface in non‐ideal reacting gases with dust particles in [11].…”

Section: Introductionmentioning

confidence: 99%

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On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

Singh,

Shah,

Jena

2023

Math Methods in App Sciences

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In this manuscript, the advancement of one‐dimensional shock waves propagating through a non‐ideal reacting gas is examined. Considering the shock wave as a propagating discontinuity surface, a pair of evolution equations describing the strength of the shock and the first‐order discontinuity for variable initial data are obtained. The truncation approximations are used to obtain the exponent of shock velocity for the case of strong shock with constant initial data and compared with those exponents obtained from Guderley's scheme and Chisnell–Chester–Whitham (CCW) rule. The effects of non‐ideal and reaction parameters on the shock evolution in the case of arbitrary shock strength are examined and compared with those obtained from the CCW rule. Furthermore, the global behaviors of shock strength and induced discontinuity for different values of non‐ideal and reaction parameters are analyzed.

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“…where Ω = (m∕x) x=X and v = u s − Π. With the help of equations ( 6), (9), and (10) (2,3) , we get the nonlinear differential equation describing the shock strength [u] as…”

Section: Evolution Equation For Shock Progressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

Singh,

Shah,

Jena

2023

Math Methods in App Sciences

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show abstract

“…Gupta and Jena [11] explained the kinematics of the spherical shock wave in interstellar gas clouds and Mehla and Jena [13] studied the effect in a relaxing gas due to the presence of dust particles. Shah and Singh [14] discussed the evolutionary behavior of non-planar weak and strong shock waves propagating into a non-ideal relaxing gas by using the kinematics of one-dimensional motion. The approximation method was used by Lee [24] and Van Dyke and Guttman [25] to solve the initial value problem of propagation of shock waves by expanding the solution in the powers of the time, where Chisnell [26] used the theory of singular point to explain the propagation of shock analytically.…”

Section: Introductionmentioning

confidence: 99%

Shock wave kinematics in interstellar gas clouds with dust particles

Chauhan

Arora

2022

Preprint

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In this article, a system of partial differential equations governing the one-dimensional motion of an inviscid gas with solid dust particles is considered. The evolutionary behavior of cylindrical and spherical shock waves in dusty gas is determined. To accomplish this, we used a technique that is based on the kinematics of the one-dimensional motion of shock waves. This allowed us to derive an infinite hierarchy of transport equations that describe the strength of shock waves and the induced discontinuity behind them. These equations are used to determine both the decay and growth behaviors of shock waves in dusty gas. Considering the first two truncation approximations, the results so obtained are compared with the results obtained by Guderley’s exact solution and CCW approximation.

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Evolution of acceleration waves in non-ideal relaxing gas subjected to the transverse magnetic field

Nath,

Kadam

2024

J Eng Math

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Propagation of non-planar weak and strong shocks in a non-ideal relaxing gas

Cited by 9 publications

References 15 publications

On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

Shock wave kinematics in interstellar gas clouds with dust particles

Evolution of acceleration waves in non-ideal relaxing gas subjected to the transverse magnetic field

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