PROPAGATION OF SHOCK WAVES IN GASEOUS MEDIA GOVERNED BY QUASI-LINEAR HYPERBOLIC SYSTEMS OF PDES

Abstract

This thesis addresses the detailed analytical and numerical investigation of the so lutions of selected hyperbolic systems of quasi-linear partial differential equations. Chapter 1 is introductory, providing an overview of the subject matter that has evolved over time. Chapter 2 The purpose of this study is to obtain the solutions using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the axial mag netic field. Here, isothermal flow is considered. In the undisturbed medium, varying magnetic field and density are taken. Out of four different cases, only three cases yield the similarity solutions. Numerical computations have been performed for the cases of power-law and exponential-law shock paths, to find out the behavior of flow variables in the flow field immediately behind the shock. Similarity solutions are obtained by taking arbitrary constants in the expressions of infinitesimals of the Lie group of transformations. Also, the study of this work provides a clear picture of whether and how the variations in the non-ideal parameter of the gas, Alfven-Mach number, adiabatic exponent, ambient magnetic field variation index, and gravita tional parameter affect the propagation of shock and the flow behind it. Chapter 3 is focused on studying the shock waves propagation through an ideal radiating gas containing solid dust particles of arbitrary strength. To analyze the shock front kinematics, an infinite set of transport equations determining shock strength and induced discontinuities is obtained. A truncation approach of the in f inite system of transport equations yields an efficient shock propagation system of f inite ordinary differential equations. The analysis appropriately reflects the nonlin ear steepening effects of the flow behind shock fronts due to the dynamic interaction between shock fronts and the flow behind them. The effects due to dust param eters and radiation on shock propagation are discussed with the help of graphical representations. The decay laws for weak shocks in a non-radiating gas are pre cisely recovered by the second-order truncation approximation. The characteristic rule, the first- and second-order approximations, are compared for shock waves of arbitrary strength.