Weak discontinuities in one-dimensional compressible nonideal gas dynamics

This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles.