In this paper, we study the collision of a one-dimensional steepened wave with a blast wave for the system of partial equations describing the unsteady flow of dusty real reacting gases with the same γ-law. The real gas is characterized by a van der Waals type equation of state. Special attention is devoted to analyzing the effects of real, reaction, and dusty gas parameters on the steepened wave. The amplitudes of the reflected and/or transmitted waves along with the jump in shock acceleration after the interaction are also obtained.In this paper, we study the collision of a one-dimensional steepened wave with a blast wave for the system of partial equations describing the unsteady flow of dusty real reacting gases with the same γ-law. The real gas is characterized by a van der Waals type equation of state. Special attention is devoted to analyzing the effects of real, reaction, and dusty gas parameters on the steepened wave. The amplitudes of the reflected and/or transmitted waves along with the jump in shock acceleration after the interaction are also obtained.

Collision of a steepened wave with a blast wave in dusty real reacting gases

In the present paper, we study the Riemann problem for quasilinear hyperbolic system of partial differential equations governing the one dimensional ideal isentropic magnetogasdynamics with transverse magnetic field. We discuss the properties of rarefaction waves, shocks and contact discontinuities. Differently from single equation methods rooted in the ideal gasdynamics, the new approach is based on the system of two nonlinear equations imposing the equality of total pressure and velocity, assuming as unknowns the two values of densities, on both sides of the contact discontinuity. Newton iterative method is used to obtain densities. The resulting exact solver is implemented with the examples of general applicability of the proposed approach. For comparisons with exact solution we also shown numerical results obtained by the total variation diminishing slope limiter centre scheme. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new Riemann solver.

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Riemann solution for ideal isentropic magnetogasdynamics

Evolution of weak shock waves in non-ideal magnetogasdynamics

Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves

In this paper, we studied the behavior of different modes of wave propagation and breaking of wave front by employing the theory of singular surfaces in a plane and radially symmetric flow of a non-ideal relaxing gas. The one dimensional steepening of waves is considered and the transport equation for the jump discontinuity of velocity gradient is obtained. The effects of relaxation and van der Waals excluded volume of the medium on the jump discontinuity of velocity gradient are analyzed.

One dimensional steepening of waves in non-ideal relaxing gas

Interaction of an acceleration wave with a strong shock in reacting polytropic gases

In this paper, the Lie group theoretical method is used to establish the entire class of self-similar solutions to the problem of shock wave propagation through reacting polytropic gases with the same $$\gamma $$
 -law. The system consists of two species, burnt gas and unburnt gas. Necessary conditions for the existence of similarity solutions for shocks of arbitrary strength as well as for strong shocks are obtained. The arbitrary constants, occurring in the expressions of the infinitesimals of Lie group of transformations give rise to different cases of possible solutions with a power law, exponential and logarithmic shock paths. For the existence of self-similar solutions, the forms of reaction rate are found out in different cases. A particular solution is considered to study the effect of reaction rate on the similarity exponent.

Existence of self-similar solutions in reacting gases

In this paper, we investigate the problem of imploding shock waves in dusty real reacting gases with the same γ-law via the Lie group invariance method. Necessary invariance group properties of an ambient gas for strong shocks are presented and yield the forms of the reaction rate in different cases. The collapse of imploding shocks for a radially symmetric flow of non-ideal dusty reacting gases is completely characterized. The effects of mass consolidation of dust particles, relative specific heat, van der Waals excluded volume, energies of formation of mixtures, and the ratio of the density of dust particles to that of density of the gas on shock involution are obtained.

Randheer Singh

Papers

Interaction of an acceleration wave with a strong shock in reacting polytropic gases

Collision of a steepened wave with a blast wave in dusty real reacting gases

One dimensional steepening of waves in non-ideal relaxing gas

Existence of self-similar solutions in reacting gases

Imploding shocks in real reacting gases with dust particles