Evolution of C1 -wave and its collision with the blast wave in one-dimensional non-ideal gas dynamics

Abstract

The aim of the present paper is to analyze the collision of discontinuity wave with blast wave in non-ideal gas flow through Lie group approach. The particular solution of the system of quasilinear hyperbolic PDEs, governing one-dimensional unsteady cylindrically symmetric motion in non-ideal gas, is obtained. The equation governing the evolutionary process of weak discontinuity in non-ideal gas is derived which is utilized to discuss the growth and decay process of the weak discontinuity. Furthermore, the collision of discontinuity wave with the blast wave is examined inside the state described by the exact solution of the blast wave. Also, the existence and uniqueness properties of reflection and transmission coefficients of the waves along with the discontinuity in the shock acceleration are discussed. © 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.