Browsing by Author "Rahul Kumar Chaturvedi"

Now showing 1 - 9 of 9

Evolution of weak discontinuity waves in non-ideal interstellar environments
(Springer, 2023) Shweta; Rahul Kumar Chaturvedi; Shobhit Kumar Srivastava; L.P. Singh
A systematic method is used to study the problem of propagation of planar, cylindrically symmetric and spherically symmetric shock waves of the one-dimensional motion of an inviscid, self-gravitating, non-ideal interstellar gas cloud. The analytic solution of the problem is resolved, which specifies non-linear behavior in the physical plane. The transport equation, which describes the evolution of weak discontinuity in non-ideal gas is derived. It is observed that the nature of the solution completely depends on the net volumetric cooling rate and self-gravitating parameter. It is observed that an increase in the value of self-gravitating parameter results in delay of process of shock formation and shock forms early when heating dominates cooling in the system. Also, expansive waves take less time to decay in planar geometry as compared to cylindrical and spherical geometries and compressive waves take more time to develop shocks for cylindrical and spherical geometries as compared to planar geometry. © 2023, Indian Academy of Sciences.
Propagation of nonlinear wave in 2-D planar and axisymmetric non-ideal radiating gas flow under the influence of magnetic field
(Springer, 2024) Shobhit Kumar Srivastava; Rahul Kumar Chaturvedi; L.P. Singh
Influence of magnetic field on the propagation of shock waves in radiation gasdynamics is analysed by using wavefront analysis method. We examined behavior of the waves propagated into the two-dimensional (2-D) steady supersonic magnetogasdynamic flow of non-ideal gas with radiation. The transport equations are derived, which determine the condition for the shock formation. The effect of non-idealness and thermal radiation and their consequences under the influence of magnetic field is studied and examined how the flow patterns of the disturbance vary with respect to the variation in the parameters of the flow. It is found that the presence of a magnetic field plays an essential role in the wave propagation phenomena. Nature of the solution with respect to Mach number is analysed, and it is examined how the shock formation distance changes with an increase or decrease in the value of Mach number. Also, the effect of non-idealness on the shock formation distance is elucidated and examined how the shock formation affects the increase in the value of non-ideal parameter in the presence of magnetic field with thermal radiation. © 2023, Indian Academy of Sciences.
Shock wave solution for the planar, cylindrically, and spherically symmetric flows of non-ideal relaxing gas
(Elsevier B.V., 2022) Shweta; Rahul Kumar Chaturvedi; L.P. Singh
In the present article, we investigate one-dimensional non-ideal relaxing gas to study solution of shocks for planar and non-planar flows, more specifically cylindrically symmetric, and spherically symmetric flows. The analytic solution of the problem is determined in the characteristic plane. It signifies that linear solution in this plane reveals non-linear behavior in the physical plane. Also, the condition of shock formation has been determined by analyzing the growth and deterioration of shocks using transport equations. It is observed that nature of the solution completely depends upon relaxing gas parameters and non-idealness. All computations are done using computational package MATHEMATICA. © 2022 The Physical Society of the Republic of China (Taiwan)
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.
The growth and decay of nonlinear wave in polytropic reacting gas with small solid dust particles
(Elsevier B.V., 2024) Rahul Kumar Chaturvedi; Shobhit Kumar Srivastava; L.P. Singh; Nilam Venkata Koteswararao; Akshara Makrariya
The aim of this study is to examine the evolutionary process of shock waves along the characteristic path under the effect of dust particles in a polytropic reacting gas. Testing the nature of the governing quasilinear of this system as a coordinate, we reconstruct the governing equations as Bernoulli's differential equation and obtain the results. The results in the characteristic plane can display a non-linear behavior in the physical plane. It is shown how the reacting gas parameter influences the evolutionary process of the compressive and expansive waves, respectively, in reacting gas flows. Also, it is shown how the existence of dust in reacting gas influences the growth and decay of the compressive and expansive waves. The transport equation leading to the evolution of shock waves is determined and used to derive the condition for the shock formation. The comparative study of the effect of reacting gas parameters and dust particles on the flow patterning and distorting of shock waves for planar, cylindrically and spherically symmetric flows is also performed. © 2023 The Physical Society of the Republic of China (Taiwan)
The Riemann problem for one-dimensional dusty gas dynamics with external forces
(Taylor and Francis Ltd., 2022) Shobhit Kumar Srivastava; Rahul Kumar Chaturvedi; L.P. Singh
This article concerns the study of the Riemann Problem (RP) for a non-homogeneous system governing the one-dimensional compressible flow of dusty gas, where the external forces are assumed to be continuous function of time. The elementary wave solutions such as rarefaction wave, shock wave, and contact discontinuity are rigorously determined. The effect of dust particles on the density and flow velocity and shock speed is examined, and their consequences on the solution of the Riemann Problem are discussed. Moreover, we discussed the condition for the existence of vacuum appears in the solution of the Riemann Problem. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
Weak discontinuities in one-dimensional compressible nonideal gas dynamics
(De Gruyter Open Ltd, 2022) Shobhit Kumar Srivastava; Rahul Kumar Chaturvedi; Lal Pratap Singh
This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles. © 2022 Walter de Gruyter GmbH, Berlin/Boston.