Browsing by Author "Pradeep"

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Evolution of shock waves in dusty nonideal gas flow with magnetic field
(Walter de Gruyter GmbH, 2024) Shweta; Pradeep; Shobhit Kumar Srivastava; Lal Pratap Singh
This paper deals with the study of propagation of shock waves in 2-D steady supersonic magnetogasdynamics flow of nonideal dusty gas using wavefront analysis method. We derived the transport equation, which determines the condition for the shock formation. Our aim is to analyze the effect of interaction of dust particles with magnetic field in nonideal gas on the evolution of shock formation and to examine how the flow patterns of the disturbance vary with respect to the variations in the physical parameters of the medium. It is found that the presence of magnetic field plays an essential role in the wave propagation phenomena. The nature of the solution with respect to the Mach number is analyzed, and it is examined how the shock formation distance changes with an increase or decrease in the value of Mach number. Also, the combined effect of nonidealness, magnetic field, and dust particles on the shock formation distance is elucidated and examined how the formation of shocks is affected by the increase in the value of corresponding physical parameters. © 2024 Walter de Gruyter GmbH, Berlin/Boston.
The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem
(Institute of Physics, 2023) Gaurav; L.P. Singh; Pradeep
This paper reports the solution to the Non-homogeneous Riemann problem by applying the approach of differential constraint for the one-dimensional (1 − D) generalized Chaplygin gas equations with non-constant initial data. Here we take source term as a Coulomb type constant frictional term. We reduced the governing non-homogeneous model into a homogeneous one by introducing a new velocity variable. By virtue of this advantage of frictional type source term, we would easily determine the solution of reformulated homogeneous governing model. We have computed the differential constraint and its consistency conditions for the specified model. Moreover, we have derived here the compatibility condition between the governing model and the differential constraints. The solutions to generalized Riemann problem for the 1 − D Euler’s equation of governing gas model are obtained as well as for the smooth and non-constant initial conditions the comprehensive overview of the solutions is studied. © 2023 IOP Publishing Ltd.
The concentration and cavitation in the Riemann solution for non-homogeneous logrithmic equation of state with magnetic field
(American Institute of Physics Inc., 2024) Pradeep; Rahul Kumar Chaturvedi; L.P. Singh
In the present study, the phenomena of concentration and cavitation in the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field is analyzed. Firstly, we introduced new state variable for the velocity to modify the non-conservative system into conservative system and solved the Riemann problem for modified system constructively. Further, the Riemann solutions for the transport equations is investigated as pressure and magnetic field vanish. It is proved that the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field having two shock waves converges to the delta shock wave solution of the transport equations as pressure and magnetic field vanish. It is also proved that the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field having two rarefaction waves converges to the contact discontinuity solution of the transport equations as pressure and magnetic field vanish. © 2024 Author(s).
The effect of dust particles on the evolution of planar and non-planar shock wave in two-dimensional supersonic flow of van der Waals gas
(Springer Science and Business Media Deutschland GmbH, 2022) Pradeep; Rahul Kumar Chaturvedi; L.P. Singh
The motive of this study is to investigate the impact of the dust particles on the shock formation in two-dimensional steady supersonic flow of the composition of van der Waals gas and small solid dust particles for the planar, cylindrically symmetric and spherically symmetric cases. It is shown that the governing equations describing the van der Waals gas with dust particles is hyperbolic in nature. Further, by employing the method of wavefront analysis, we derived the transport equations for shock wave which lead to derivation of shock formation distance and also, provide the relations of shock formation. Also, it is determined as how the shock formation distance is affected by the presence of dust particles, parameter of van der Waals gas and upstream flow Mach number (M> 1) by using MATHEMATICA 11 software. © 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
The formation of shock wave in a two-dimensional supersonic planar and axisymmetric non-ideal gas flow with magnetic field
(Springer Science and Business Media Deutschland GmbH, 2021) Rahul Kumar Chaturvedi; Pradeep; L.P. Singh
This paper presents an analysis of the of the shock formation in 2-D steady supersonic flow of non-ideal gas with magnetic field for the planar flow and axisymmetric flows. It is shown that the governing equations describing the non-ideal gas flow with magnetic field is hyperbolic in nature. Further, using the theory of the propagation of wavefronts defined by weak shock, we derived the transport equations for shock wave which lead to determination of shock formation distance and provide the conditions of shock formation. The formation of shock wave is affected by the presence of magnetic field, non-ideal parameter and upstream flow Mach number M> 1 is shown. © 2021, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.