STUDY OF SHOCK WAVES PROPAGATION IN GASEOUS MEDIUM

Abstract

Gas dynamics is a branch of hydrodynamics, the study of uids, liquids, and gases, which arose towards the end of the nineteenth century as a result of attempts to understand the principles of high-speed compressible ow theories. The shock wave is a mathematically and physically interesting phenomenon and it has been a very important research topic for the last few decades. One of the main reasons for this is that it has many examples of applications in various elds. In aerodynamics, the knowledge of shock waves is extremely essential for designing the optimal geometry of objects moving faster than the sound velocity, e. g., supersonic aircraft or spacecraft reentering the atmosphere of planets. In material science, shock waves are used to induce phase transitions or chemical reactions. A typical example is the transformation of graphite to diamond induced by a shock wave. In astrophysics, the supernova explosions and collisions of clouds are typical examples involving shock waves. In the eld of medical science, there are numerous applications of shock waves, for example, the kidney stone in a human body can be destroyed by a weak shock wave generated by \Extracorporeal Shock Wave Lithotripsy (ESWL)". We start with a brief review of shock-waves in which the shock associated with hyperbolic systems of conservation laws is identi ed by its front, i.e., a moving surface that divides the space into two subspaces in which a continuous solution exists but where there is a jump in the eld variables across the shock front.