STUDY ON SHOCK WAVES PROPAGATION IN GASEOUS MEDIA AND SYMMETRY ANALYSIS OF COUPLED EQUAL WIDTH WAVE EQUATION

Abstract

Gasdynamics is a sub eld of hydrodynamics, which is the study of uids, liquids, and gases. It emerged at the tail end of the nineteenth century as a consequence of e orts to comprehend the fundamentals of high-speed compressible ow theories. The equations of gasdynamics have traditionally been used to study shock wave propagation. The phenomenon of shock waves is mathematically and physically interesting, and study into them has been extremely important over the past few decades. One of the primary reasons for this is that it can be applied in a wide variety of domains. In brief, a shock wave is a non-linear wave that travels faster than the speed of sound in the medium. Shock waves occur frequently in everyday life, although they go unnoticed the majority of the time. Physically, the emergence of a shock wave in a uid ow is always characterized by instant changes in the ow velocity, pressure and temperature. This change is not reversible; inside the shock wave, dissipation of energy occurs and the entropy increases. Shock waves have gained much importance due to instantaneous changes in velocity and pressure, and are being investigated for potential applications in a variety of elds. In the eld of aerodynamics, when designing the optimal geometry of objects moving faster than the speed of sound, such as supersonic aircraft or spacecraft re-entering the atmospheres of planets, having an understanding of shock waves is extremely important. A shock wave can promote the transition of graphite into diamond, which is a classic example of this phenomenon. In the eld of astrophysics, two common scenarios that involve shock waves are the explosions of supernovae and the collisions of clouds. Numerous applications of shock waves may be found in the realm of medical science. One such application is the removal of kidney stones from the human body using a technique known as \Extracorporeal Shock Wave Lithotripsy (ESWL)", which involves the use of relatively modest shock waves. To begin, we will conduct a quick review of shock waves. In this type vii viii of wave, the shock that is associated with hyperbolic systems of conservation laws can be identi ed by its front. This front is a moving surface that divides the space into two subspaces in which a continuous solution exists but there is a jump in the eld variables across the shock front. The existence of shock waves was predicted by considering certain waves traveling in a uid governed by the Euler equations.