The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

Abstract

This paper reports the solution to the Non-homogeneous Riemann problem by applying the approach of differential constraint for the one-dimensional (1 − D) generalized Chaplygin gas equations with non-constant initial data. Here we take source term as a Coulomb type constant frictional term. We reduced the governing non-homogeneous model into a homogeneous one by introducing a new velocity variable. By virtue of this advantage of frictional type source term, we would easily determine the solution of reformulated homogeneous governing model. We have computed the differential constraint and its consistency conditions for the specified model. Moreover, we have derived here the compatibility condition between the governing model and the differential constraints. The solutions to generalized Riemann problem for the 1 − D Euler’s equation of governing gas model are obtained as well as for the smooth and non-constant initial conditions the comprehensive overview of the solutions is studied.